So the first thing I plan to do with this game is do the misc trilogy any%.

Would I be able to take the individual game runs from that and submit them to the normal game categories, or would that break some sort of rule?

I don't really see a problem here because looking at the individual games you're completing them (with respect to some percentage goal) according to the board rules. Might want to wait for a mod to answer though.

Yes you can as long as you submit the correct times for each individual run.

WhitePaaws PB'ed Crash 3 105% during a 305% race with me recently and it got accepted, so it would only make sense for the same to be allowed for NST.