I just want to clarify that there are actually 8 TR variants: Throne Room, King’s Court, Counterfeit, Procession, Disciple, Royal Carriage, Crown and Ghost. (Counterfeit can be played by Storyteller and play Crown, so is relevant.)
Of course Donald made the point that the TR variants are not really the problem.
Trivialknot actually deserves a lot of credit for
this post, where he identified that the problem is with any card being moved after having been played. And this is also the first scenario presented which is impossible to resolve IRL, because the player him/herself can't know the answer to what the card actually is. (In the other examples it was possible to keep track of the Estates in your hand.)
It seems like the only workable changes would be:
1) Actually change the three offending cards (Inheritance, BoM, Overlord).
2) Always use last-known-info as suggested by ChipperMDW. (Although I don't like the idea of reverting BoM to choose-before-play, because that created a lot problems compared to how cleanly it works now.) The problem is that it changes the Procession+BoM-as-Fortress explanation in the original Dark Ages rulebook, and probably other "known" interactions, which could be unexpected for many players online whenever it would change there.
3) Introducing a rule like I think Majiponi suggested, that whenever there is doubt about which copy of a card you're playing, you get to choose which. But what if you only have one copy among your cards, so that from a computer perspective there is no choice, but from the players' perspective how many copies you have is not open information (and a player might or might not have kept track)? Maybe that's why Donald said it wouldn't work.