Let's assume Lost Arts and BoM apply both at the same time, on-play, before the card effect happens. Shouldn't you be able to decide what happens first, meaning that you can effectively have it either way (including the option to not get an action*)? Mysteries above mysteries...
To me the only way to interpret BoM is that the instructions happen
before play.
When-play instructions, like Moat reactions for instance, happen after the card has hit the table, and Lost Arts falls into this category:
"When you play a card from that pile, you first get +1 Action."So it seems that the card you play is actually the card you chose (and not "BoM"), when you resolve Lost Arts:
1) Choose to play BoM.
2) Resolve the before-play instructions: Choose Sea Hag, and set up the card to be Sea Hag from the point it's in play to it leaves play.
3) Play the card, turning it instantly into Sea Hag.
4) Resolve any when-play instructions:
- (4A) Lost Arts gives +1 Action if there is a token on the Sea Hag pile.
- (4B) Players can reveal Moats.
5) Resolve the card's instructions, which are Sea Hag's instructions.
The effects in step 4 are simultaneous, but we resolve the current player first, so +1 Action happens first.
Maybe we could consider
"BoM turning into Sea Hag" as a when-play instruction instead, but that would mean that the BoM is first played as a BoM (step 3), and Donald's statement contradicts this. ("You cannot play a BoM.")
In order to also get the effects of a +1 Action on the BoM pile, (4A) needs to also check the BoM pile. That would mean that the card (even though it's not a BoM) is "from" the BoM pile while at the same time it's "from" the Sea Hag pile. It seems a little strange to me.