The theme seems to be strictly "onboard assets", but generators are made to be assembled independently. I want to be able to have characters who express emotions, but in order to do that, utilizing the generator is the only possible tool I can use.

So is it No Custom DLC Parts Allowed, only the generator that came out of the box?

Correct. No DLC usage, at all.  With a little work, you can show different emotions with the generator that is included, with most RPG Maker engines.  I have done this before.