Hi Lee.
As already stated above, your old cardboard FAA 'Piggyback' (61.75) Certificate is no longer valid.
You will have to go to CAA at Gatwick and get it updated to the new plastic Certificate, and have the number changed to your new EASA Licence number.
Then, so long as you have at least a Class II Medical, a valid Type/Class rating, and have completed a BFR with an FAA Instructor, you are, as they say across the water, 'good to go'.
On a more general note:
My understanding is that all the old Licences are still ICAO compliant, and as such are still valid (with an appropriate Medical and Class/Type Rating) for flight on non-EASA registered 'EASA' aircraft outside of EASA.
It follows then, that, so long as you already have the new plastic FAA 61.75 Certificate, it should also still be valid (with a valid BFR) on US registered aircraft, outside of EASA.
I'd welcome any thoughts on that!
MJ