Here's my take on Claimant. With it around you might want to be more careful about emptying piles.
Couldn't it be shortened to "Gain a card costing up to 5$ from a supply pile that has at most 2 cards in it"?
I think it's not a very useful effect, though, because the requirement is fullfilled too rarely, and I would probably have done better trying to get those cards using Silver than by using a Copper+ that will rarely, possibly reward me.
Monastery feels like a bad Workshop. I mean, yes, it will be able to gain one or two Golds if you put some effort into it, but that's not enough to counter the fact that it can be completely useless if you draw it with another terminal and no Village. I don't think I really like the Gold gaining effect much here nor on New Explorer.
I like the idea of Lodge, though.
Sage could also be buffed, even though the +1 Card on it doesn't have the problems that terminal +1 Card usually causes. Anyhow, to buff it, you could make it a Treasure, so you can use it to topdeck that Village you drew dead with your Smithy. See my Decree for a dimilar effect.