At uiuc, it’s harder to get into engineering as an internal transfer than as a freshman. If you can’t get direct admit, odds are very very low you’ll get into engineering from chemistry.
You’re better off trying to find colleges within budget where you’d get direct admit to engineering.
If you’re not competitive for uiuc you won’t get into Georgia Tech.
U Wisconsin is more flexible.
Look at Missouri M&T, Iowa State, UMontana.