The snag is with a TRE you need to hold the appropriate instructor and type rating for the type on which you are examining. The instructor and type rating on which you instructing are on your Part FCL licence which requires a medical to be valid. So no medical, no licence and the TRE certificate is invalid.
I got an SFI/SFE on the basis on my TRI/TRE (just in case) from the Dutch. The CAA have historically refused to issue the SFI/SFE until you lost the medical. I'm amazed some NAA are turning a blind eye to the whole medical bit. What else do they not get?