My situation is slightly different from the usual. I have lived in the US 20 years and for the first 15 or so I flew entirely on a 61.75 based on UK/EASA. My rule of thumb was not to do anything I was not CURRENTLY entitled to do in both countries. Anything else you may not discover the legal position until the court case. The one exception is you are probably ok with just an FAA medical although to renew / revalidate EASA you now appear to need a medical anyway so you can't sustain that very long.
The issues have been much discussed on PPrune but they are certainly not clear. Some have even argued your licence is not even VALID without a medical. As has been said good luck (to you or your lawyer) with getting the answer you want from the CAA.
At the moment to fly again in the UK I would have to get an ATO recommended training schedule and pass a skill test and probably a few other things - the idea that I could reactivate my 61.75 with just an FAA medical and a (B)FR would seem to be more than a stretch. If you are living outside the US maybe you can afford to take a more sanguine view of potential liability issues.