I think that the meaning of "it" is key here. In the blue dog discussion, the reason Ironworks doesn't give you +1 Action if you Ironworks an Ironworks then reveal a Trader is that "it" refers to the particular physical card that was gained, NOT to a card name. So because you did not actually gain any particular Ironworks, you don't get the +1 Action, even though the Ironworks remembers that you wanted to gain something named "Ironworks".
So here, I think the "it" on Throne Room must be referring to the particular physical Band of Misfits card, not to the card name "Feast".
On the other hand, imagine that TR does play BoM as a Feast the second time. Then, there is no particular physical card that Throne Room is playing; it's not playing BoM, because BoM does not think it's a Feast anymore. To me, that goes against the general interpretation of "it" in Dominion.