I haven't seen anyone mention the "Observation" skill. I've got a custom military tab in Dwarf Therapist with leader, teacher, student, observer and concentration. I've noticed that every dwarf in my military, and almost every immigrant with military skills, also has observer at the same level as their other military skills. All of my active military also have concentration at the same level as student.
If Toady is giving ALL immigrant soldiers the observation skill, it just might be important for quickly training military. Just sayin', ya know?
Also, I've had the best luck training with squads of 2. All of the training is applied to 2 dwarves, giving them 1 or 2 months of "no orders" will cancel the "long patrol", even if you issue a move or kill order in the middle of their vacation. My starting military (5 Armor + 5 Teacher, 5 Dodger + 5 Teacher) were Axelords in just under a year, with 17 and 19 in fighting. They did have a lot of combat (harpies and ogres and badgers, oh my), but never had an injury after the 1st harpy attack (no armor, no weapons, no duh they got hurt). Larger squads with a minimum less than the squad size will only train some of the dwarves at any one time, and will spend a lot of time waiting for everyone to assemble.
Part of the issue is that while some players have figured out how to get training to work, nobody has been discussing what NOT to do. What are bad practises which must be avoided to speed up training? Why is it that some people spend years of training and only have 2 skill level gains to show for it while others make huge leaps?
From what I can tell, mixing different weapon types in a squad slows down training. Paying attention to Student/Teacher skills also helps greatly.
Don't assign mail shirts AND breastplates OVER clothing. Most dwarves won't be able to wear everything, and armor will be left behind. Or they'll do the stockpile dance.
Don't assign helms and caps if you haven't finished making the caps. You'll end up with dwarves wearing helms without caps, and head protection is arguably the most important.
Don't expect raw recruits to be legendary in a month, unless you're using a danger room. Noobs train slow, and get pwned by everything.
Don't mix weapon types in a squad (as Psieye and others have mentioned).
Don't put active miners, woodcutters, or hunters in the military; their hidden uniform will mess with equipping.
Don't put peasants in the military, they'll get a bad thought at the start of every month when they (briefly) switch from mil to civ and back to mil.
JMZ
You're gonna need more dorfs! Manually operated pumps only power themselves, you can't transmit "extra" power anywhere, because there is no extra power. You'd need 170 dwarves pumping at the same time to move a reasonable amount of magma.