When you're talking at the levels that most engineering positions are paid pretty much anywhere in the US (even lower cost of living areas), you are unlikely to qualify for need-based aid anyways. A pay cut from (lets say) 200 -> 150 is significant, but I don't believe likely to qualify a student as "low income" by any means.
Stanford covers all tuition for parents whose income is $125k or less, and partial tuition for parents making more than that until some cutoff. Regardless, $150k would be getting you a decent bit of financial aid.
It would depend on how much of a pay cut you experience moving to Spokane, but that can certainly make colleges with extensive need-based aid cheaper.