>The EASA licence can only be valid when the relevant EASA medical is also valid.
Not true. Don't confuse validity with currency or medical status or exercise of privileges.. Valid means 'not suspended, revoked or withdrawn' - the presence or absence of a medical certificate does not affect validity..
As far as the FAA is concerned, to use the privileges of a 61.75 certificate, an ICAO compliant medical or an FAA medical are equally acceptable.
To answer the question properly one would need to know the country you propose to fly in and the country of registration of the aircraft. Also you mention a class 2 and a class 3 medical, but don't say which country issued which.
On the assumption that you are trying to fly in Oakland or similar on an N reg, either a class 2 EASA or a class 3 FAA medical is acceptable to use with the 61.75. You must comply with FAA currency / flight review requirements etc. You do not need to simultaneously meet any such EASA requirements.
If you are in europe then it is more complicated, and depends on the registration and where you are actually based and what/how you are trying to fly.
Hope that helps