Agreeing with everyone here who said "play tablestuck", if you want to play sburb Id highly recc that you play a ttrpg with sburb mechanics in them. Learn from my mistakes, its much more simpler to use a system that supports the kind of game you want to play over trying to hack and chop up a system and bending it into doing what you want.

For the second problem of "not wanting to separate the players", I would second what HC said, with trolls flarping and hanging out together. If I were you, I'd figure out what *kind* of homestuck story you want to tell. Do you want to do sburb? Do you want to play with trolls? If so, are they going to be kids or adults? I say figure out what kind of "homestuck game" you want to play and work from there.