Reely - you say: "The final question is what happens when after acquiring a piggy back lic and maintaining a recent enough BFR all my EASA TRs have expired, from FAA's point of view?"
I think that's covered above in response to Claudia's similar question: "As per the legal opinion issued by the Office of Chief Counsel for FAA quoted above, "...the FAA has not considered the absence of a rating as a restriction on a person's pilot certificate." So the revalidation of the type ratings in the 'parent' license, via a proficiency check, is irrelevant to the validity of the 61.75 'piggy back' license. The requirement is only that the license itself remains valid (which, being not time limited is not hard to achieve) and that a valid medical supports the license. So an EASA type rating that has expired (i.e. not been revalidated) does not constitute a limitation on the EASA license such that it limits the validity of the 61.75 certificate based upon it."
So, in short, nothing happens (to your ability to fly an N reg aircraft on your 61.75 certificate) if your EASA type ratings expire, so long as you retain your FAA BFR, logbook endorsement and appropriate medical. Indeed, I suppose nothing would happen either if your EASA type ratings expired before acquiring a 'piggy back' certificate, because, as we know, a "missing EASA TR" is not a "limitation" in the FAA's sense of the word.
As ever, I am no authority, I've just read the legal opinions and talked to some instructors and examiners. Am happy to be proved wrong by any one of the many people that told me and apparently continue to believe that: "...the 61.75 certificate covers only the type’s on your UK license."