I don't think your are overlooking anything, I can confirm all your assessments.
All the incorrect cases seem baffling, because they seem really simple. If only turn 10 was incorrect, one could think it has to do with automatically (incorrectly) going to the buy phase, but turn 8 proves that is not the case.
I already have an instance of Royal Carriage/Vassal in the known bugs list, this seems to be an extension of it, I have to look into it in detail.
I know that in order to present a good UI for Royal Carriage in case of chains, there had to be some work done and maybe that gets into problems here.
ADDED: On further reading the old bug reports, it seems what you found is exactly another instance of the problem described there. If you play Vassal from your hand using an Action, it considers itself 'played' way to early. That means in your case that happens before the Royal Carriage is even played, so under that incorrect understanding of "played" for the Vassal, Royal Carriage can't be called.
If you play the Vassal by some other means (Golem, or as you did, Throne Room), this problem goes away, for unknown reasons.