Are you applying to Questbridge? This could be your best way in to your top reach schools, i.e. MIT and Cornell, plus quite a few more top-tier ChemE programs at QB partner schools. (Stanford, Caltech, Princeton, Johns Hopkins, Northwestern, Rice, UPenn, CWRU, BU, Tufts, Notre Dame, USC,UPenn, Vanderbilt, WashU, Yale…)
Does the budget statement mean that you’re actually able to pay up to 50K/year, in spite of the $0 SAI?
Have you run the Net Price Calculators for the schools on your list?
Presumably you’d be eligible for the Excelsior Scholarship at the SUNY’s, yes? I’d include SUNY Buffalo in addition to Bing and Stony Brook; its engineering programs are very strong. (Plus they have linguistics and even an undergrad computational linguistics major, should your secondary interest become primary.)
In terms of OOS publics, Delaware is well-known for ChemE (ranks #4, above UIUC, for undergrad programs), and they have some large merit awards that you’d have a chance at. They have a great Honors College, with some interesting Scholars programs including a Grand Challenges Scholars program for engineers.
Goergia Tech is, of course, excellent, but the only large scholarship for OOS is the Stamps full ride, which is possible but highly, highly competitive.
Given your high SAT, any chance you’re also a National Merit Semifinalist?
Carnegie Mellon is another strong ChemE school that meets need, but is not a Questbridge partner.
Run the NPC for UMich. I believe they used to give some need-based aid for OOS low-income students, but I’m not sure what the current policy is.
I’m not sure what the path to affordability would be at UIUC, UW-Madison, and Purdue.
With such strong options in the SUNY system, I don’t see why you should go out of state for much less than a full ride, even if you do have a source of funds to pay more. There are definitely possibilities for full-ride need-based aid or merit. But among the schools where your costs will be significant even with merit, I would think very hard before giving up an essentially-free education either via Excelsior, or from a full-need-met school.