Officially if you accept a Downgrade they don't have to allow you into the lounge but in practice they will do whatever it takes to keep you happy.

Unless you really want to be downgraded to PE there are plenty of options tomorrow.

BA is selling J seats via other cities to either IAD or DCA, including via DUB to IAD. One advantage of connecting through DUB would mean that you vlear US CBP in DUB. When you get to the US you simply land at a domestic gate and walk off the plane and out of the airport.