I've now done some fairly extensive testing of Piggy Bank and Archivist, which I've renamed Coin Collector and Museum, respectively.
Coin Collector ("Piggy Bank" in the original post) seems to play fine. I took into account WW's thought that it was too strong, and Kn's thought that it was too weak. But it seemed to play okay. I think all it needs is to gain you a Prize AND a Duchy, rather than one or the other. The reason is that it does take a good while to cash in*, by which time you probably don't want a Prize over a Duchy anyhow. Plus, you will probably only get to cash in once, so boosting the reward isn't as dramatic as it would be with, say, Tournament.
*With one exception: To avoid the issue of not drawing Coin Collector and your last Copper together, open Coin Collector/Silver and don't buy much of anything until your CC is cashed in. You pick up the 8th Copper on a turn when you've used CC and thus can't buy much else anyway. You can buy a 9th Copper on such a turn to reduce the chance of bad draw luck later. When you cash in the CC, you'll have virtually no money in your deck, but that's okay: you just pick Bag of Gold or Trusty Steed as your prize, and that will correct your treasure shortage -- which more than compensates for those early turns where you bought nothing at all. With this strategy, gaining a Duchy as well actually weakens you a little (a good thing), as it slows down your now very trim but powerful deck.
If you use CC solely for the trashing ability, it's strictly worse than Chapel, so no problem there.
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Museum (previously Archivist)
This is too weak as originally stated. You have to work too hard for 5 uniques that you don't mind trashing. Not only does this mean trashing a couple of good cards you spent turns accumulating, but you're also spending five whole turns building up to a Prize or Duchy, which is almost certainly a losing strategy.
If you use it only for its trashing ability, it's even worse: all the trashing it does that's useful is one Copper, one Estate, and sometimes one Curse, and you spend as many turns to get there. Later in the game, you can stow away a Province and a Duchy too, which is somewhat useful on late-game turns where you're clogged with green and can't do anything better anyway, but it's not a game-changing move even then.
So, as with Coin Collector, I boosted the reward to a Prize and a Duchy. I also knocked the requirement down to just 4 unique cards, which is a whole lot more manageable. A couple of use cases:
(1) You stow away a Copper, an Estate, and a Curse. Now you only need to stow one more card away to gain a Prize and a Duchy. Since a Prize and a Duchy are virtually always going to be better than the weakest card in your card at any given time, it's no problem if the fourth card you stow away is a good one. Probably it's just a Silver, which is no great loss.
(2) You open Museum/Museum, stowing away a Copper, an Estate, and then one of your Museums. Just one card to go, which is, as in case (1), no problem.
(3) You stow away a Copper, an Estate, and the Chapel you've been using in parallel to trim down. Just one card to go.
The point here is that finding 3 cards to stow away is easy. It's what you have scrape together beyond 3 that's hard. Reducing the requirement from 5 cards to 4 is a more dramatic change than it seems.
I still need to play with this one some more, but I think these changes make it more balanced. It's still not something you always want to go for, but in certain situations it's a lot of fun. Even just the Island-like capability of it is fun on its own: you can get one copy of each Victory card out of your way, which encourages you to buy different ones.