How about this wording:
"Reveal any number of Coppers from your hand and set them aside; +$1 for each Copper set aside. At the start of your next turn: discard all set-aside Coppers; +$1 for each Copper discarded."
This gets rid of the Mint/Mandarin issues, and removes the overpowered continuous-hold Coppers problem, but doesn't somehow change the wording on the Coppers themselves, and uses methods of keeping track that already exist.
That's not bad. And I'm all for not changing the wording on the Coppers themselves. Zahlman's point that this renders Barge un-stackable is a good one, thought, which probably weakens it a bunch. What if we split the difference—play Coppers this turn, discard them next turn?
"At the start of your Cleanup phase this turn, set aside all Coppers you have in play. At the beginning of your next turn, discard the set-aside Coppers, and +$1 per Copper discarded by Barge."
I still suspect this is a $3ish Action.
