I am not sure if the OP already has a piggyback, but this statement is incorrect:
Your piggyback will not be valid unless your EASA licence is valid.
FAR 61.19(c) states...
The holder of a pilot certificate issued on the basis of a foreign pilot license may exercise the privileges of that certificate only while that person's foreign pilot license is effective.
An EASA licence remains "effective" if it has not been suspended or revoked, regardless of whether the ratings on the licence are valid or not.
Provided the holder of a piggyback certificate issued under FAR 61.75 has completed a flight review under FAR 61.56 and complies with the recency requirements of FAR 61.57, he can use that certificate to fly a N reg aircraft even though his EASA ratings are not current.
The same applies to medical certificates. Provided the pilot holds a current FAA medical, he does not need a valid EASA medical certificate to fly a N reg aircraft.