thank you!! yes i was suprised with how hard it was to find smaller engineering schools that offered more than stem, but i guess it makes sense in hindsight lol. rice was unfortunately the best match i had found for a smaller school that was in a diverse city w/ chem e. (twin cities would be higher than madison in this regard, but it would cost about $6k more, so…)
as for my local safeties, they don’t actually offer chemical engineering, iirc madison and point are the only ones (in state) that do. i applied with materials engingeering and biomed, but that was mainly because i wanted to have options if i decided to stay close to home. i am somewhat considering the materials engineering school, but its not high. i can dm you that one if you would still like though!
and for iowa, that was more of a last resort for me (no offense to those who love the school…). i would just rather go to madison, between the two of them. thank you still for the suggestion though 
definitely, the progression requirement is a worry of mine. i dont think i had the strongest science background, particularly in regards to labs, and ive heard freshman physics is especially difficult at madison. although, i was thinking that since i will have completed the calc sequence beforehand, the upper level math classes might help me balance my core gpa a little bit? since i wont have to take the notorious calc two… 