Can't you just get into the sphere of UK or something, and let them deal with Qing?
Your population is too large for the UK to influence, coupled with the fact that it is impossible for you to be sphered in time before the Qing have sieged down all of your holdings - their troops start on your border and in sufficient quantity that at least half of your infantry have to retreat or will be immediately killed. To make matters worse, even if the UK was friendly, they cannot intervene in the civil war casus belli, the same way they cannot in the USA vs Confederacy war. I managed to do it by going back to the previous start date, before the rebellion begins. Thus I failed my original objective but my conclusion is that playing as the Taiping Heavenly Rebellion two months before they died is not enough time to alter the material circumstances, much in the same way that trying to win WWII as France when the Germans are in Paris is not exactly a likely prospect.
So instead I started as Qing China. Playing consecutively day after day, I refined my strategy until I found the method which worked. Each time I failed for different reasons. Sometimes the Qing government was too powerful, many times I would be carved up by Russia or Britain, even Japan. When I at last managed to get population consciousness just right and the circumstances of the civil war perfectly, I found to my horror that it was bugged. It should be the case that whoever wins the war inherits all the reforms and substates held by the other, but it actually sets all the substates free and sets the Heavenly Kingdom back to square 1 - no reforms, no cores on all of China. This meant my task would become immensely more difficult.
My solution was to Westernize the Qing government and unify all of China, and then win the civil war as the Heavenly Kingdom. This itself presented some issues. The first was that this required a lot of research points, and my population literacy was abysmal, even with my best efforts to promote the clergy and education. The second was that after Westernizing, all of the substate armies would be disbanded, meaning I would need to have a powerful enough army to deter the usual suspects (UK, Russia & Japan) but not powerful enough to render the Taiping Heavenly Rebellion a hopeless endeavour. This would be especially pertinent, since the Qing armies would be partially westernized, whilst the Heavenly Kingdom armies would be worthless in direct combat.
Conquering Asian countries allowed me to vastly increase my Westernization process through the modernization of the Qing army. Annexing Korea, Vietnam, Laos, Cambodia, Burma, Brunei and so on rapidly brought my army up to scratch - not to any Western standard, but certainly enough to overwhelm all Asian peers. It did however bring me into conflict with Japan who became a Great Power (and indeed became one of the world's top industrial powers in short time, even bringing all of Western India into the sphere of influence, holding a colonial Empire from Africa to Borneo). Subsequently I lost much land to Great Power invasions, which was all right, since the land I lost still gave me truces with the Western powers whilst protecting the core Chinese lands. Borneo fell to the Dutch, Burma would fall later to Britain, while the Japanese would be repelled after a disastrous landing in Korea - reinforcements to my islands deterred any further attempt by Japan to annex me.
Complete Westernization helped drive my population consciousness up and annexed all the substates (Tibet as a vassal was not annexed). Gradually I began amassing an army comprised of Nanfaren and Beifaren infantry from the Taiping core lands, whilst decreasing the size of my Manchu units, until the Qing dynasty was dependent upon Taiping brigades for its physical security.
When at last the Taiping Heavenly Rebellion broke out, I had a rather daunting task at hand, but I had the best chance I'd ever get. I had 15,000 infantry in Burma, 15,000 infantry in Vietnam, 15,000 infantry in Korea, the rest of my 354,000 infantry were poised to seize the capital and the big population centres in the heartland of China. Resistance was fierce, with the Qing able to amass 180,000 Western-standard soldiers in the Southwest of the Empire, around Chongqing and Vietnam. My Vietnam brigades were defeated almost immediately, but managed to retreat to join the main force. The Burma brigades were considerably more successful, tying down 2x their number in the mountains. With 45,000 troops taking the North and Korea, everyone else focused on pushing Westwards. Time was on the side of the Qing, as the more time they could buy the more their qualitative superiority and higher population would inevitably wear my forces down. Subsequently every time the Qing forces attacked, I diverted my attention towards defeating their stacks. It was painful, as I had 2 generals to split between all my armies, and I'd always end up losing at least 2x more troops than the Qing in every battle. Nevertheless it ensured I never lost momentum in sieging down the Qing Empire.
But after 3 years, it was at last over. I'd lost a lot of men, but the population I gained from the Qing Empire's collapse more than made up for it. At once I set about reforming the education system as I realised I had to Westernize all over again, and began amassing troops to garrison my borders with the UK and Russia. I stood no chance against either of them, but it did help give me some more peace of mind ;]
As before, as today, I lost a lot of my territories to various Western powers, but gained more land in central Asia. These are the borders I kept for the rest of the game. One issue is that I had no cores for everything, so in order to core it all I had to become a great power. Upon Westernizing my #1 priority was researching nationalism & industry, in short order my Heavenly Kingdom was building railways everywhere and flooding the world with cheap iron, coal and agricultural produce. Under the auspices of the Reactionary Faction I built up cement and steel factories everywhere, distinctly aware that I was entering into the world market and the industrialisation game horrendously late. Fortunately I had sufficient, vastly overwhelming stores of wealth from tariffs alone, that I could amass a gargantuan army (rapidly becoming the #1 military power, above Britain) whilst subsidizing a whole swathe of unprofitable factories - at least, unprofitable at first. As a low ranking civilised nation I had little access to world markets, so had to rely upon China's own vast wealth. I had sulphur, iron, coal, silk, and subsequently became world leader in luxury clothes productions once my own domestic cotton industry kicked off. Once I had enough stores of processed and raw materials, a sizeable industrial base and a growing population of craftsmen, I switched to the conservative faction to let them expand industry at their own leisure - only switching back once in order to build up my automobile and electronics industry.
It was just before WWI that I broke into Great Power status. My industry began to skyrocket whilst my military expansion increased at an unabated rate - for efficiency's sake I'd increase my army in batches of 600 brigades, bringing them all into Taiping before crudely sorting them mixed regiments of infantry, dragoons, artillery and engineers. I rapidly began coring most of my country, which at this point was just flooding with Chinese people, who made coring even Korea, Mongolia, Vietnam and Central Asia a trivial task.
With my industry and economy of scale overwhelming my competitors, my industrial science catching up and exceeding my rivals, the European powers ravaged by Great Wars - it opened up the opportunity for America & Japan to sphere much of the world. The Americans, Japanese and British had far too much influence on countries bordering me, so I decided to change that by challenging them all on their turf. I could flood countries with so much foreign investment that the other Great Powers couldn't match, so it resulted in things like a quarter of South America falling under my sphere of influence. Challenging America and Britain was a mistake, at least that early on. Although my industry surpassed them, my Navy was still using sailships and my army was not a match for either. When I annexed Tibet the British and Americans joined forces to enforce the status quo; I learned quickly that my forces were still no match for Britain's. Fortunately I got away intact, ending the war early by releasing Tibet under the American sphere. In the meantime I fortified China and modernised my army.
During the Second World War, I figured the other Great Powers would be to busy to notice me annexing Tibet. I was right, however it pushed my just slightly above 25 infamy. Two years after the Second World War ended, the British invaded, in the British war to contain the Heavenly Kingdom. This time however, they found my troops dug in, within trenches, Fortresses, with artillery and machine guns, engineers and limitless reserves more than a match for their own. I was capable of sending hundreds upon hundreds of brigades without ever having to underman my core or my Russian borders, and if I absolutely had to I could recruit thousands or mobilize 5,000+ brigades. As far as land wars were concerned I had at last reached the point where defensively I was mostly secure.
...Mostly, I did nearly lose a war against Russia. The Italians dragged me into a war against the Austro-Hungarians, I ended the war by giving away Italian land and ended my alliance with the freeloaders. I could have easily won the war if I was willing to sacrifice my men against Russia but I had nothing to gain from making Italy more powerful at my expense, especially while I was making the transition into becoming the foremost industrial power in quantity AND quality.
While this may look like a lot of rebels, I usually swung between 5-7 million active soldiers who would use the railway networks to crush rebellions of this size within 1-2 weeks. Also notable in the pic, is that it was my first use of my armoured brigades - my tanks effortlessly crushed the rebels and soon accosted the British, confirming their fall and my ascent as the world's foremost power. At this point I tried to see if I could make my Navy as strong as my Army, but while I got up to steamships I realised I'd never get a Japanese or British navy in time before the game ended, I contented myself with making a large air force and armoured brigades, especially once all the Middle Eastern oil fell under my sphere of influence. I occasionally intervened in European politics - my favourite one being when I made Germany win WWII by flooding them with war subsidies, making their war go from -70 to victory, cutting subsidies once they outlived their usefulness.
By the end my power was confirmed; when it came to industry or land power, everyone else was fighting for second place. And while my prestige wasn't as good as my industry or military, I was rather pleased that the more prestigious powers like Germany continued to bleed prestige in disastrous wars. With even Spain, Turkey and Portugal under my sphere of influence, the Western Indian states allied with me against British Imperialism, I had at last built up a force which could actually overcome British defences and liberate India.