If OP and family decide they do not want to pay Cornell’s price at this time , OP can decline the acceptance. There is a stiff price for doing that in that it could be the best deal in terms of selective college and price. I’ve seen people lose out that way.
Financial aid at HPY does tend to be more generous.
I agree with most everyone here that the OP has a sweet deal and the GC was what one gets with GCs. That’s the way they act regarding selective college applications. They have a good idea who is going to be accepted and in fact control a part of the process.