You're right that Distant Lands could be interpreted as checking where it was when the game ended. But the thing is that doing that check is in itself an activation of the ability under the line on Distant Lands, so clearly the effect of the card is still active during scoring. Of course this is also the case with Landmark abilities that say "when scoring"...", or indeed for cards that simply say "6 VP" for instance, like Province. These are all effects that are active during scoring.
I don't see how it could be any other way for Inheritance according to a strict reading of the rules. Of course Donald could rule the other way and it would be clear and unambiguous. It would just be a special ruling. And actually that is the case for BoM/Overlord-as-Duration on the last turn. According to a strict reading of the rules, it should count as that Duration and not as a BoM, but Donald has ruled that it's a BoM.
Having written all that, I'm going to admit that I could be wrong in one sense. There actually is another strict reading of the rules which would revert Inherited Estates to just Estates (and revert BoM to BoM without a special ruling). And it's what I mentioned in my last post, involving Distant Lands, which you observed could be interpreted differently: If we say that all cards are supposed to be moved into your deck before scoring*, then the card that has the Estate token will lose it. Also, Distant Lands move from the Tavern Mat, but then we'd have to first remember how many were on the mat (in case there are some in the deck already). So we have to count some cards before we start scoring, which is somewhat inconsistent.
* It's unclear to me what is the current ruling on this. New rulebooks and cards talk about your cards at end game rather than cards in your deck, so clearly it's not supposed to matter where the cards are anymore.