Suggestion: The game uses Gestalt rules. Why? So that you have more room for shenanigans.
Basically, what I'm thinking is, you reserve one "side" of their progression for advancement in their game Aspects. This should require some form of spellcasting-style mechanic, since these powers seem to be heavily supernatural. At character creation, before any role advancement happens, it can be used for weird abilities characters have by virtue of being themselves. Trolls should use it for their psionic powers, if any, while humans should use it for their own particular superpowers, like Dave's super-speed, Jade's oracularity (that is so definitely a word, spellcheck) later retrained to Witch of Spacely spellcasting, or Rose's Bardic Knowledge. I recommend starting below level 4, so that characters who want to start without any supernatural powers have that option by selecting classes like Ranger or Paladin, which don't grant spellcasting until higher levels. Spells/powers/what-have-you known should be chosen based on their Aspect.
The other "side" of their progression should be reserved for their game Classes, and should forbid any sort of full-spellcasting progression (to help enforce the division between Class and Aspect), but should allow partial casters like the Bard for characters who want to be heavily supernaturally themed (in a deep irony, Gamzee would probably not actually be a Bard).
While you are creating a division between Class and Aspect here, remember that characters are an organic whole, so it's okay to take levels or abilities on one side that really contribute to the other. Similarly, you should also allow qualification for PrCs and such by looking at the entire character, not arbitrarily dividing their qualifications by side somehow or something. I also put "side" in quotations earlier because technically, Gestalt rules don't track that, but it's a handy way of thinking about this sort of idea.
Anyway, I haven't got time to actually play in it, but I love shaping mechanics to fluff so there's my suggestion for that. Good luck to you!
EDIT: Side effect is that either everyone writes Human down on their race line (even trolls, because they're differentiated by their choice of classes), OR everyone can write down whatever humanoid they want and you just file off the serial numbers.