I playtested this in a real game (2-player) a few days ago. It was an amazing amount of fun, since it makes you completely rethink all the other cards it appears with. I really think I'll have to play several more games to get a handle on it. However, my initial thought is that it needs to cost $7. It's not that dissimilar, when you think about it, to an Expand (Pearl Divers become Peddler-with-a-bonus cards; Markets become Grand Markets; terminal Silvers become terminal Golds), the difference being that ALL copies of the upgraded card get upgraded, with the drawback that one of the copies is permanently removed from your deck.
My opponent and I used the card on Markets and Merchant Ships. I went for Merchant Ships first, then Markets, while my opponent went directly for Markets and never used it on anything else. Markets are obviously super good targets for it, which I was slower to catch onto, but Merchant Ship turned into a power card too. Then I had to go Markets anyway for the +Buy.
Cantrips in general would be prime targets, as simple cantrips become Peddlers, and Peddlers become activated Conspirators. In the absence of those, I imagine it would do interesting things to other non-terminals like Apprentice. Anyway, more experimentation is required, but it's really cool.
One drawback is the swinginess of having to collide it with the action you want to set aside; however, this actually isn't THAT bad, since whatever action card that is you probably want multiple copies of. So you buy multiples at the outset, and the necessary collision will be inevitable.
In turn, that does mean you probably play decks without a lot of variety, which is perhaps a minor aesthetic drawback, but I think it's well worth it. Great idea!
Edit: I'd recommend adding wording about returning the set-aside action cards to your deck at the end of the game. If you couldn't do that, it would be the only such card not to have the cards return (Native Village, Island, maybe Haven fits), and it would be more fun with Vineyards, Gardens, and dual-type Action-Victory cards not to lose them.