My understanding is that if you fly relying on the U.S. "Airmans Certificate" which is dependent on your EASA licence then your EASA licence must be fully valid. The EASA licence can only be valid when the relevant EASA medical is also valid. I don't understand why the Italian NAA couldn't be clearer but of course they cannot authorise flight in the USA using a USA certificate.
There are numerous FAA offices throughout California, they are the only reliable source for you. Could just be a phone call away.