While I agree OP should call and ask for more merit aid, most private schools are not motivated to match pricing of public schools. And that’s saying it nicely…private schools generally couldn’t care less what a student’s FA offer from a public school is, regardless if it’s in or out of state.
I encourage OP to not mention UConn when speaking with GWU, and just ask for more merit aid by saying if you can get to X price my child will commit. GWU is not known for negotiating much either, so go in with low expectations.