I'm following this with great interest as a US-based pilot, with FAA IR (and N-reg plane too) who will probably one day move back to Europe.
Couple of comments for what they're worth...
1. Class 2 FAA mdical is essentially identical to Class 3. My last one I asked at the last minute "what would it take to get a Class 2?", since I was thinking of doing my CPL (still am) and didn't want to waste the time if I couldn't get the medical. "Oh," said my AME, "I just tick this box instead of this one". And I had a Class 2. There are a couple of very minor things, but I think the main difference has to do with how they deal with exceptions. Even for Class 1 the only difference was that I'd have had to do an ECG.
2. Seems to me that an FAA IR is worthwhile anyway just because from a flying pov an IR is an IR and it's not a bad thing to get the training done. The CAA IR is obviously ridiculous in its non-flying requirements but who knows whether anything will ever be done about it - it seems to me that the US is the only country where private flying is officially viewed as anything but a serious nuisance.
3. On car registration: I very happily operated a French reg car in London for several years, occasionally popping back to France for convenience and legality. They got me in the end by changing the rules for residents parking permits. However if you live outside a major town then that doesn't apply.
n5296s