This thread seems a lot more confusing than necessary.
OP, can you please run the Net Price Calculator for Syracuse and tell us what your out-of-pocket would be with their normal need-based aid? Net Price Calculator
The only way need-based aid is going to give you additional money after the yellow ribbon $ is if your net cost is lower than the costs that are left over after the full tuition scholarship. (And if that’s the case, you’d have gotten that much aid even without yellow ribbon - the only difference is that SU might be more inclined to accept you, since they’re need-aware and the VA funding would relieve them of paying a big chunk of your aid.)
You have some good in-state schools in Oregon. Do you have a favorite that would be attainable and affordable? Is there a school you could commute to from home?
What actual financial resources do you have? The guaranteed loans you can take on your own will cover only an average of $6750/year. What do you estimate that you could pay per year?