I agree; I was wrong on the medical side.
However it still leaves us with the need to move the foreign-reg planes to the registry of an EASA member state, which involves certification on that registry.
Incidentally I think that EASA will ultimately have no choice but to accept FAA certification completely (*). Otherwise, their published proposal to subject all EU-based planes to the EASA maintenance regime will not be possible. But that is yet another obstacle which is at least a few years further down the road after the DfT has finished over here
(*) The national certification authorities (CAA in the UK) will really hate that because they won't have anything to do; they will just have a man sitting there issuing an AAN for every STC that comes in the post.