Mmmm... I guess having the ability to specify exact deities is OK, although it kind of ruins the surprise of random procedural stuff, so long as random procedural stuff still exists...
Although what I was kind of hoping for would be to recreate the plotline of Touhou 11: Subterranean Animism.
First, you find a dead avian sun god, and feed it to a hell raven to make her a
nuclear-powered hell raven with the rediculously awesome superpower of "
Nuclear Fusion", giving her the power to generate suns, and throw them at people. This should also turn the hell raven/demon into a humanoid form, while you're at it, preferably with a big, red, Sauron-like eye in her chest.
Second, hand off the job of "taming" the hell raven onto some shmuck of an adventurer who now has to save the world from the monster you created, then left to run amok. This adventurer must literally venture into (one of the) Hell(s), fighting off absurd numbers of unrelated demons, to find the hell raven, and defeat her in single combat. This takes not only absurd amounts of
convection shmonvection for the ability to fly through the mantle of the planet to get to (with only a complaint about how unseasonably warm it is in the Hell of Blazing Fires) the hell raven, but then, having to stage a fight where the adventurer must continually dodge the suns the hell raven generates by flying through the corona of the suns, somehow dodging the heat and light and even radiation they eminate. (Perfect playthrough demonstration of this found here:
http://www.youtube.com/watch?v=BQLIaZUOnBU (actual fight starts at 2:06) very impressive, you should watch it.)
Third, take the "tamed" psuedo-goddess, and stick her in a cage or a bottle or something, and turn her into a nuclear fusion reactor just so you can brag about how you just did someting those stupid humans and their "modern techonology" couldn't do, by making a working fusion reactor. Then use it as a handwave excuse to power all sorts of electrical equipment you steal from the modern human world so that you can start introducing characters later on who have cell phones.
(Sorry to bring up Touhou fairly often, but I like Touhou for the stupidly over-the-top crap they do, and it really sounds more like the stuff that dwarves would do (or, at least, funnier) than much of real mythology, which was mostly about sex and rape and revenge for rape, anyway.) (edit: Well, actually, I kind of dislike regular mythology since I tend to feel really sorry for most of the monsters, many of which were unwanted and abandoned children or else normal human women who were "punished" for being raped by having their entire families slaughtered and being transformed into monsters for "heroes" to come along and kill. At least Touhou ends with them sipping tea.)
Now, in order to do this, however, we need the ability to defeat gods without killing them, though, which sort of leads to the whole "gods shoudln't die from cheap tricks like obsidian casting" thing. Maybe it could be something like a Lich's phylactery, where killing a god physically just makes them vulnerable to having their true power source destroyed, where they will come back if you don't actually take that final step. (So you can bring them down to vulnerability, and then force them to share power or bind them in your service rather than outright destroying them.)
Of course, that would require some sort of special exemption from "deletion" mechanics, like obsidian casting or cave-ins. Even if we allow cave-ins to be fatal, there would still need to be a way for some object to remain nearby, or a way of saying "there's something inside this obsidian wall".