Chance me for MIT, UCSD, UChicago, UIUC [SC resident, 3.81 UW, 34 ACT, math/cs, single parent household, <$30k (35000 SAI)]

I agree but I think if it’s math and not CS, UIUC is likely but at $54K tuition, room and board and no merit coming, what’s the point - as you noted.

There are sub schools (yes, won’t be as high on a US News ranking) that come in within budget.

UIUC and the UCs are wasted energy, money and time in applying, and just no. But the sub schools work - and that’s what OP should consider - schools achieving the budget, not schools that sound great on paper but are well past what they can spend.