I think throne room explicitly acts on cards, and I think that BoM is one of those cards that is affected by the whole "while this is in play" thing. Like highway.
As I understand it, throning a highway doesn't reduce costs by $2, because it goes down like this:
1. Play throne room, moving it from hand to in play.
2. Choose highway from hand
3. Play highway, moving it from hand to in play
4. Play that same highway, not moving it because it is already in play.
Conclusion: There is only one highway in play. It was played twice.
When playing with cards I feel this is like playing the highway, then picking it up, then playing it again. So the card's instructions happen when it hits the table, and throne room causes it to hit the table twice (though it never leaves play).
I sort of feel like BoM throne rooms itself. When you play it, the instruction is to play it (again) as a different card. It stays in play, turns into a different card, and I play it again (from in play).
As for the throne room-BoM question, I think you pick once for normal cards, twice for cards that remove themselves from play. Throne room specifically says that you play the CARD (that card) twice. BoM refers to that same card (this card) with its transformation and replay.
So throne room-bom-smithy would be like:
1. Throne room, from hand to play
1.1. Choose the second card in my hand that is a BoM
1.2. Play that second card.
1.2.1. That card becomes a smithy
1.2.2. Play that card.
1.3. Play that second card again (from play). It never left play, so it is still a smithy.
But throne room-bom-as-feast would be:
1. throne room, from hand to play
1.1. Choose the second card in my hand that is a BoM
1.2. Play that second card.
1.2.1. That card becomes feast.
1.2.2. Play that card (from play)
1.2.2.1 Trash that card. (it becomes BoM in the trash)
1.2.2.2 Gain a card
1.3 Play that second card again (from the trash, since throne room doesn't lose track of feast, it shouldn't lose track of BoM). It moves from trash to in play.
1.3.1 That card becomes smithy (or anything)
1.3.2 Play that card (from play)
Is there another way to reconcile it with how "while this is in play" interacts with throne room/kings court?