I'm quoting you out of order so that I can address points in a logical fashion.
But really, my concern is mainly with how strong it can be with higher player counts. We don't really think about the 3p game or *shudder* the 4p game much on f.ds, but it's still something that should be considered when designing fan cards. Did you test it with 4p and good Estate trashing like Chapel or JoaT?
I don't think it got testing in 4-player games, but I play mostly 3-player games and occasional 2-player games. In most games players buy 1 or 2 Cemeteries. When a player tries to pursue it as an alternate Victory strategy, a Cemetery rush is initiated that often cannot be won by a significant enough margin to make continuing to build it up worthwhile.
What I think you are overestimating is its inherent value. Cemetery is pretty worthless until other players chip in to make it valuable. Cemetery presents a similar problem to
City in that way: The threat of a player trying to power-up Cemetery is enough to initiate a Cemetery rush (a rush that, of course, makes Cemetery a better card), and you have to win the split by a large amount to make building them up at all worthwhile.
With 2p and decent trashing available (possibly counting itself), you can expect this to be worth 3VP as both players trash their starting Estates. That makes this a $3 Duchy, which seems a bit dangerous to game balance to me. It's more of a concern with more players. In 3p you can expect it to be worth 4VP, in 4p it'll be worth 6VP. A $3 Province seems rather swingy. This is without considering possibilities like buying and trashing Estates (especially with Watchtower) if you win the split by enough.
I can confirm that "itself" is not good enough trashing even at its low price point to ensure every player's Estates will end up in the trash. Most games would end with Cemeteries being worth 2VP or 4VP in 3-player. The reason players would still have Estates is because there are only so many times you can spend $3 on a Victory card in an earlier portion of the game, and spending $3 to trash one Victory card for another Victory card, while possibly initiating the Cemetery rush is not worth it--especially considering how much one has to win the Cemetery split by to make building it up viable.
Counting all Victory cards seems like a harmless buff. It often doesn't matter, but it's a bit better with Shelters and offers a somewhat interesting decision when you buy a Cemetery when you have another in hand. Is it worth trashing your Cemetery to remove the dead card, but potentially making opponents' Cemeteries better? It can also matter with various trashing attacks and TfB.
I think counting any trashed Victory card would be far too frustrating and swingy in
Swindler and
Knight games (wherein someone can "win" the Cemetery split by a large margin by trashing other players' Cemeteries while pushing Cemetery's value upward via the trashing) and would exacerbate leads in games with flexible trash-for-benefits like
Salvager and
Remodel, allowing players to power up Cemeteries while draining available points to other players.
Then there is the weird fluctuation from Duchies, Cemeteries, etc. coming back out of the trash with
Graverobber and
Rogue...
Counting all Victory cards seems like a harmless buff.
Rebuild disagrees.
Nice catch. That would be one exception that could make Cemetery much more powerful, but it also probably makes Rebuild games more interesting. How do you incorporate it into the strategy? In a non-mirror, can the non-Rebuild player plan to load up on Cemeteries to catch up? This seems like more of a positive point for the change than anything.
I think it would just make whoever wins the Cemetery split win the game.
Play
Rebuild, name Cemetery because who cares what you trash, it makes your Cemeteries better!
Depending on what you intended with this card, the increased cost may be undesirable because it makes the card just a little less effective for trashing. On the other hand, that puts the emphasis back on its potential VP value.
If you increase the cost of Cemetery, it would probably be a rare instance when once could afford to buy it for only trashing, it could only ever be bought for its Victory points.
The problem that you're not taking into account is its communal nature. By the time you have 4VP
Dukes, you have at least 12VP in your deck. Not so with Cemetery: Cemetery's value is equal for all players; not based on the composition of your own deck. If you're building up Cemetery, you're increasing every player (who owns a Cemetery)'s points.
Consider the best case scenario in 2-player where you win a Cemetery split 6-2. Realistically, if this happens, you've trashed your starting 3 Estates, but the other player probably hasn't trashed all of his, so Cemeteries are probably only worth 2VP, so you're a big 8VP up (and seriously, only 12VP even if all starting Estates were trashed) for 4 additional dead cards in your deck. Now you can work to make Cemetery more valuable by getting more Estates and trashing them. Every time Cemetery goes up a level, you gain 6VP, but that is comparatively 4VP against the other player. But then remember that to level up Cemetery, you're spending 2 Buys\gains to get the Estates and yet more turns and deck manipulation (or prayer) to trash those Estates, which then costs you 2VP! You go through all that work to get 6VP - 2VP - 2VP = 2VP (For a 3-player example, how about a 6-4-2 split, where you're now
helping the guy with 4 Cemeteries since he's not doing any work for the points against the 2-Cemetery player and you're not even gaining any points on the 4-Cemetery player in so doing, though we are looking at a much more profitable 4VP per Cemetery in this example).
I think it would work better by increasing the cost to $4 and counting every 3 Victory cards.
Making Cemetery worse at both trashing and being a Victory card would make the card as dead as the people in it.
I'm really not sure that Cemetery is a good or fun card, but its communal nature makes it interesting.