As I am sure you know, Delaware has an absolutely fantastic ChemE program. So much so I would personally find it hard to recommend many other programs to a person who was in-state for Delaware.
I’d be particularly unsure it would make sense to consider publics where you would have to pay a lot more OOS. I’d actually be more inclined to check out the NPCs at places like MIT, Stanford, or Princeton, just to see what they say about costs.
All that said, I agree you could also check out Minnesota. That is another great program and I believe with merit aid it would at least be closer to in-state at Delaware.
Purdue is also relatively inexpensive OOS, although ChemE is not necessarily one of their top specialties. But if you were not sure about ChemE specifically that may be a good option.
But otherwise, this could be a short list situation, which is fine.