I would like the Mint/Poor House opening a lot better if there was a $3-4 Village or something that could give you a coin (like Oasis, Tournament, Candlestick Maker). As it is you immediately have to start putting treasure back in your deck just to get to $5. Minting Copper turn 3 is a big mistake, you bought the Mint to kill those.
I think it's possible to delay the Mint here until you have added a few $5 and then get several treasures in hand with a Library draw. And with Graverobber you can buy Mint a few times to get rid of all the treasures.