I don't believe you are without an FAA IR/MEP as the FAA does not recognise EASA as a "country" for the purposes of FAR 61.3(a)(1). Had you retained your UK/JAA licence you would have been legal in the UK, but not elsewhere in Europe.
Correct, this would be an illegal flight as you are breaking FAA rules not EASA rules.
For this flight to be legal, you would need FAA ME rating, and if in IMC an IR issued by the FAA. The only time this flight would be legal is if flying in the airspace which issued the EASA license and ratings, then you would not need an FAA certificate.
As mentioned, the FAA chief council did a ruling on whether the JAA (at the time) constituted one "country" with respect to the FARs. The Chief Council's ruling was that it did not.