I'm late to this thread, and others have already said most of the things I would. But here's one card that jumped out at me as a problem:
Inheritance – Action – 4$
+2 Cards, +2$, “When you would discard this from play, instead, you may put this on the bottom of your deck.”
A card that was merely +2 Cards and +$2 would all by itself be a ~$7 card. Basically you can think of +1 Card as being roughly as powerful as +$1, though one might be rather more powerful than the other in any given situation. You can tell this based on what your average card value is. It's $0.7 at the start of the game, usually well above $1 or even $2 in the mid-game, and drops again once you start greening.
Anyway, just by looking at the base treasure cards, you can tell that each extra +$1 results in a price jump of about $3. Similarly, you can see this same increase when you compare Moat and Smithy. Moat is +2 Cards AND an extra benefit, so figure that a card merely offering +2 Cards should cost less than $2. Smithy, meanwhile, offers +3 Cards and costs $4. So again, approximately a $3 price jump.
Now, how much should +2 Cards, +$2 cost? Start with a reactionless Moat, assuming a cost of $1. Now throw in +$1, raising the price to $4. Do it again, raising the price to $7. Alternately, start with Smithy. Swap out one of the +Cards for +$1. Now add another +$1, increasing the price by $3 to $7.
You have to take calculations like that with a grain of salt. The cost scale is not linear, and the overall effect of a card might strengthen or weaken the power of any of its individual effects. Nonetheless, a card that is merely "+2 Cards, +$2" is very simple and well-understood; thus, calculations like this will be more precise than they would with something more exotic.
Anyway, so you have this $7 card and throw on its "when you discard" effect. To be able to drop the price down all the way to $4, this effect had better be a huge, huge drawback. In fact, it is not. At the beginning of the game, and any game with heavy trashing, you'll be able to play this card about as often as you would anyway. At first glance, I thought this would cause the card to miss every other shuffle, but it really doesn't. In fact, I think it speeds up the frequency with which you get to use it.
If it's at the beginning or middle of your deck when you first shuffle it in, you get to use it and then use it AGAIN on that same shuffle. If it's at the end, the reshuffle happens during the hand you draw it (either as you draw that hand or after playing the card), and then you STILL get to it again faster than you would if you had merely discarded it normally after play.
So basically in all cases, the card is played more frequently. The "When you discard" clause is a clear benefit, thus raising the power level of the card further. Though costs are more negotiable at the upper tiers, it seems like $8 might be reasonable. That's pretty crazy.
I think if you knock out one of the +Cards or one of the +$s, you'd have a fine $5 card on your hands. I guess I'd prefer to lose a +Card, for two reasons: (1) to differentiate it more from Smithy, and (2) because the official cards seem to value terminal $ slightly more than terminal draw (compare Moat to Duchess), and I'm not sure the "when you discard" clause is enough by itself to cross the critical $4->$5 price gap.
Testing will help you figure this balance out. I'm kind of interested to hear how the "when you discard" behavior feels in an actual game.