I wouldn’t think the standards at Rose Hulman or Purdue would be so different from some of the other schools you list. (Of those schools, the CoE at UIUC would almost certainly have the highest.)
Honestly, I don’t know enough to be able to accurately assess your scores. Your ACT is quite good, somewhat higher than would be expected from your GPA. Your GPA (unweighted is the most important) is good but not very good. (Rigor of courses taken also matters; you indicated that you’ve taken lots of AP classes, so hopefully that’s high.) So you get one view looking at your ACT, another from your GPA, and I don’t really know how to combine them.
To give somewhat of an idea, here’s data from Iowa State’s recent CDS. There’s a section indicating what percentage of freshman had HS GPAs in certain ranges.
Percent who had GPA of 3.75 and higher: 31.00%
Percent who had GPA between 3.50 and 3.74: 24.20%
Percent who had GPA between 3.25 and 3.49: 20.00%
Percent who had GPA between 3.00 and 3.24: 14.50%
…
So 1/5 of their freshman had a GPA around yours. So although most of the freshman were higher, that’s still plenty.
(Note that not all schools fill out all sections of the CDS, so you may or may not be able to get this data for other schools.)
You indicate National Hispanic Merit Scholar – I assume that means you’re Hispanic. Are you URM, or first generation? Either of those could help your admission chances. (I don’t know how much – might be worth checking into.)
As to Iowa and Iowa State, I don’t really know which is stronger. My impression is that Iowa State is better on the engineering side, otherwise Iowa, but that’s not based on any hard data. (I do know a few people whose kids have gone to Iowa State for engineering/CS – it is kinda seen as a decent, reasonably-priced alternative to Illinois schools; I also live in Illinois, if that wasn’t clear.) Not sure you could consider either of those schools safeties though.
Anyway, what this all tells me is that you might as well apply to any of these schools that interest you, and see what happens. But you should also have some other safer schools on your list. Someone suggested some other in-state publics. Well, the problem with that in Illinois is that there’s a big dropoff after UIUC. But perhaps you should apply to a couple of the other Illinois state schools, as safeties. (I don’t really know much about them.)