Basically just treat the whole operations like the marketing and entertainment engine that it is. The only places where the original spirit of college football lives on--playing purely for the love of the game and ol' [school name]-- is all the ones where there's no scholarships involved, the lower divisions, club sports, things like that.

I'd eliminate the requirement to be a student as well. If they want to have a tie-back to the university, they can still let active students join the paid team if they want, but the ones who want to focus entirely on their game can just live like regular working adults on whatever salary they end up getting. Maybe the universities could offer the same preferential enrollment for players who make the paid team and remain in good standing, give them an opportunity to earn their degree after they're done playing ball. Some might choose to get their degree and play at the same time, some might play and then get the degree, and some might play and then that's it.

(As a side note, to your point about the richest schools paying ex-NFL players to come back and play more, I think you could easily structure this theoretical paid college league as like a U24 league or something. Is the right number 23, or 25, don't know, but in general it would prevent the biggest mismatches. The difference between most freshmen and seniors is already wide enough, definitely don't need 30 year olds beat up 20 year olds.)

Course, I don't mean to only stop at football and basketball, I say treat all of D1 athletics like this. Yeah, someone who's really good at track&field or tennis or something, they're not going to make hardly any money off this kind of arrangement. Their choice probably mostly boils down to whether they were planning on getting a degree or not if sports was completely out of the picture, and how soon do they want to get started on their post-college career.