OP , there are many decent lounges for BA customers in North America.
Personally it would be one of my last considerations when choosing a connecting airport, especially when you are going to overnight before the TATL.
I'd go with ease of access to US airport, both sets of flight times and city I'd be spending the night in, way before the lounge experience.
But each to their own.
BTW another way I could justify fannying about with my connections in the US would be to take an east coast daytime flight to LHR.