In the original base game, Feast and TR had the same problem.
It was decreed by sir Donald that you could still get effects from cards in the trash, but you can only get the bonus from actually trashing the card once.
So with TR and Feast you can gain two cards. With TR and Mining Village, you can only get the $2 once.
The reasoning was that TR "locks in" on a card, so the text on the card is stored in TR's memory buffer or something like that.
But to make it more confusing, TR on Band of Misfits (choosing Feast the first time) will trash it, play it as Feast and then play it as Feast again, even though it's left play. Donald has mentioned this in the rulebook and it seems that Donald's standard line of reasoning is: Making it work like most people think it does.
Of course, we're not "most people", we're always actively searching for edge cases.
The reasoning is actually pretty straightforward (although complex). First, let's define "playing a card":
"Playing a card" is a two-step process.
1. Put the card into play (typically from your hand, but may be from elsewhere if so determined by card text, e.g. Golem).
2. Read and perform each step on the card, in order. If any step cannot be performed, continue on to the next step.
Throne Room reads:
"Choose an Action card in your hand. Play it twice."
So here's how Throne Rooming a Feast works:
1. Choose Feast in your hand.
2. Play Feast.
2.1 Put Feast into play from your hand.
2.2 Trash Feast.
2.3 Gain a card costing up to $5.
3. Play Feast.
3.1 Put Feast into play from your hand. (this is a step of Throne Room, and cannot be performed because Feast is not in your hand)
3.2 Trash Feast. (this is a step of Feast, and cannot be performed because Feast is not in play)
3.3 Gain a card costing up to $5.
If this is the correct definition, then you would, on the second play of HoP with counterfeit, put the HoP into play, from the trash; ergo, you would still have 8 uniques in play, ergo you would be able to gain province again.
Throne Room: "Choose an Action card in your hand. Play it twice."
Counterfeit: "When you play this, you may play a Treasure from your hand twice. If you do, trash that Treasure."
Both cards specify your hand as the place from which to play the card. Therefore, the first time, you put it into play from your hand. The second time, you attempt to put it into play from your hand (as a step of Throne Room/Counterfeit), but it's not in your hand so that doesn't work. We skip to the next step (the effect of Horn of Plenty, in this case).
The only situation that appears to be problematic with the above definition is Band of Misfits in the case of a Throne Roomed play that causes it to be trashed on first play. This kind of falls into dead horse territory, but I feel like going there today so here we go.
Here's what you get with TR-BoM as Smithy:
1. Choose Band of Misfits in your hand.
2. Play Band of Misfits.
2.1 Put Band of Misfits into play from your hand.
2.2 Band of Misfits is Smithy until it leaves play.
2.3 +3 Cards
3. Play Band of Misfits.
3.1 Put Band of Misfits into play from your hand. (this is a step of Throne Room, and cannot be performed because Feast is not in your hand.) Band of Misfits is already Smithy, as it has not left play. You do not perform any other effects of Band of Misfits, since it is Smithy.
3.2 +3 Cards
Throne Room has not lost the pointer to the card (it still recognizes the Band of Misfits it has played), it just can't perform certain actions on it (putting it into play) due to its location).
Here's the problem.
1. Choose Band of Misfits in your hand.
2. Play Band of Misfits.
2.1 Put Band of Misfits into play from your hand.
2.2 Band of Misfits is Feast until it leaves play.
2.3 Trash Band of Misfits. Band of Misfits has left play and is no longer Feast.
2.4 Gain a card costing up to $5.
3. Play Band of Misfits.
3.1 Put Band of Misfits into play from your hand. (this is a step of Throne Room, and cannot be performed because Band of Misfits is not in your hand.)
3.2 Band of Misfits is Feast, even though it has left play.
3.3 Trash Band of Misfits. Band of Misfits is no longer Feast.
3.4 Gain a card costing up to $5.
It seems like we need an additional clarification of this ruleset to address this situation, which is difficult to create without causing contradictions. Perhaps it could be done as an errata to Band of Misfits:
"Play this as if it were an Action card in the Supply costing less than it that you choose.
This is that card until it
leaves is discarded from play."
Now we can reconcile everything with a simple rule:
The memory buffer for cards in the Trash lasts exactly as long as there is an active pointer to them. Band of Misfits in the Trash remembers it is Feast as long as Throne Room is still using it, but as soon as it isn't, it forgets it is Feast and becomes Band of Misfits again.