Let me start by saying that I don't think this particular situation is probably going to come up a lot, but it's a good discussion to have nonetheless.
I think a lot of the issue comes from assuming that TR/BoM/Feast can be resolved by examining TR/BoM and BoM/Feast and then combining them, and I don't think that's correct. We can see that if we Throne Room BoM with any card that doesn't trash itself (Bishop, say) that's exactly the same as TRing a Bishop. No problem, it's clear from the card wording. We can also see from using BoM on Feast that it stops being a Feast as soon as we trash it. But in the specific case of Tr/BoM/Feast I think it works a little bit differently...
TR: we play 1 card twice. Note that it's "THIS card" and not "THIS BoM" which we can see from the usual TR/BoM interaction. We also fully resolve the first play before we do anything on the second play, standard TR stuff.
BoM: resolving this card fully means that it becomes Feast for as long as it's in play.
Feast: resolving this card fully means that BoM is no longer in play, which means it's back to BoM again. Right? So when we start to resolve the second part of TR... remember, we're not resolving "THIS BoM" or even "THIS BoM which is now exactly the same as Feast" but "THIS card" which happens, at the time we resolve it, to be BoM again. It's wonky, but TR/Feast has always been kind of wonky, so this just amplifies that.
My takeaway is that, in the unlikely event that you drew TR/BoM, had Feast AND ANOTHER <$5 card on the board that you wanted to play instead of Feast... you probably could. But if it gets ruled differently I'll play that way. I still don't think I understand all of the Trader corner cases so we can just add on to that pile.