I see now that Donald wrote that. But to my mind BoM is already reverted back when you're trying to exchange it. It's in your discard pile at that point. At the moment you discard it, it's a Page, yes. But when you resolve the when-discard ability, it's already in your discard pile. Compare to how "when-gain" works for Watchtower or Royal Seal. It triggers when you gain, but when you resolve it, the gained card is already in your discard pile.
So then I would say that if the criteria is just that you're able to return the card to its pile, whichever pile that might be, both BoM-Page and EstatePage should work.
I see. I was thinking that BoM would still be BoM and you would be trying to put it into the Page pile. However you already discarded it from play, you pick it up from the top of your discard pile (even though this is never what anyone does), and it's a BoM now.
So, you can upgrade BoM or Estates-Inheriting-Page. You return BoM to the BoM pile, Estate to the Estate pile.
Black Market still doesn't work (whether Page or BoM copying Page), there is no pile to return the card to.
I'm going to try pulling a 'feed the blue dog and take it for a walk' trick as per the Possession/Ironworks discussion. I don't know if it will work.
The rules say "When a player discards a Traveller from play, he may exchange it for the card indicated"
What does 'it' mean? Shouldn't it mean "the Traveller that was discarded from play"? In which case shouldn't exchanging BoM fail because there isn't a Traveller on the discard pile to exchange, merely a BoM? And even if one takes the less extreme view that 'it' merely means "the Traveller" shouldn't exchanging Estates-Inheriting-Page fail because the Estate is merely an Estate with added powers: it didn't inherit 'Page' as its name, so does it really count as a Traveller? Actually maybe it does as the rules state "Adventures has Traveller cards. These cards have an arrow over the text box to remind players of their ability to upgrade into another card." so maybe the arrow over the text box is the definition of a Traveller card. On the other hand although the rules tell us "Page is exchanged for Treasure Hunter", they are completely silent on what Estate or BoM are exchanged for, and neither Estate nor BoM are Page at the moment of exchange.
EDIT: I've subsequently realised that much of the last paragraph overlooks the fact that Traveller cards have 'Traveller' as a type, so Estate-Inheriting-Page and BoM-Page are definitely Travellers. And as Donald points out in his reply, the card text clears up the final sentence. Memo to self: always remember to look at the card text before posting.