I actually don't agree that there can't or shouldn't be other cards with the Curse type. I think it's obvious by typical Dominion wording that "Gain a ___" refers to a specific card name, whereas "If it's a ___" refers to card types. So for example, Fortune Teller or Vagrant interacts with OP's Curse type cards. I get that it might make things confusing to have a Name and Type called "Curse", given that effects in Dominion can refer to Names or Types. But, be 100% honest: is that really OP's fault? Just saying, don't blame a fan card creator for a minor flaw with the game he's designing fan cards for.
Gendo, your critiques are spot on, but I actually think that a version of Cursed Store (or really any "Curse" type card) could create a fun little mini-game where you have a really strong card that you need to get rid of before emptying the Provinces or three-piling. I kind of think of Wine Merchant, only instead of the goal being "get this thing back into my deck", the goal is "get this thing into the trash". Though as it exists currently, I agree that it's too good relative to cost. It probably needs to be changed so that it's harder to trash and so the penalty for not trashing it is higher.
If I were to design a card with that mini-game goal in mind, I'd probably 1) Playtest it with -2VP so that you're less likely to just leave them in your deck at the end, 2) Make it a Reaction, give the player a specific goal that when met allows them to trash the card, and 3) Add specific wording that prevents you from trashing it any other way (maybe something like "When you do blah blah blah, you may trash this. If you trash this any other way, put it into your discard pile")