So I'm a little late to the party, but oh well.
After doing all this reading, I have concluded that, given the cards' texts alone, Throne Room (and other 'multipliers') and Band of Misfits should behave differently when played together than the current ruling indicates. (also since the Dark Ages rulebook clearly contradicts what I'm about to say it's almost pointless for me to keep going, but I'm going to anyway, paying attention only to the text on the cards)
Choose an Action card in your hand. Play it twice.
So when you play Throne Room, you pick an Action card in hand; if BoM is in hand, TR clearly sees it as BoM, it's not a Feast or anything else while it's in your hand. So then you play that card that you chose--which
has to be BoM--two times.
Now, some of the interpretations ITT seem to be based on the idea that it goes more like this: I play TR, choose an Action card, BoM--oh BoM has suddenly already morphed into the card I'm going to play it as (say, Feast), even though I have
not yet reached the instruction to play the chosen card twice, so now I've chosen BoM-as-Feast, so now I play Feast twice.
I see no real reason for BoM to make the transformation after it has been chosen but before it has been played. TR wants to pick an Action card from your hand, BoM is an Action card in your hand, BoM should be played twice, not BoM-as-Village is played twice so it must be a Village both times. That's right, I'm saying that you should be able to pick different cards for BoM to imitate/copy/be/whatever-you-want-to-call-it.
But wait, you say, after TR has moved BoM to play, BoM has definitely become something else, like Smithy, so obviously it must be Smithy again. I disagree with this conclusion too. When you Throne a Feast, it gets trashed the first time, but is still played the second time--TR doesn't care where Feast is, it's just playing Feast. So why should TR care about 'finding' BoM again? TR shouldn't care that BoM isn't in play, or that now there's this Village in play that wasn't a moment ago; it should just follow the instructions of the
chosen card twice, which was BoM.
Weirdly this results in BoM sitting in play as the first card that it copied. So I play TR, choose BoM, first choosing a Village, the BoM card is now in play as a Village card, then second I choose to copy Embargo, I get +$2 and can place a token, but there's no Embargo card anywhere to get trashed, so I get to keep my BoM.
Conclusion: based on a strict reading of the cards alone, when you play a Throne Room/King's Court/Procession and choose BoM, you should be able to choose a different Action card to play BoM as, each time it is played. Of course the rulebook overrides this, but oh well.