There is still one more solution that I was thinking of I guess. Hint: No durations, and all the other cards in your hand are terminal actions and/or treasures. Not library, shanty, menagerie or any card that draws back up to a certain amount in hand.
The first dozen that come to mind (I'm reading the above as the card in hand can be any thing that isn't a jack/watchtower/lib/menage):
1. Counting house + copper x4.
2. Adventurer in a venture deck (venture x5 + gold).
3. Scrying pool (I don't know if this violates "certain amount").
4. Outpost (the idea being to get rid of the other dead terminals and try to draw something like menage in the OP turn).
5. Hunting party (I don't know if this violates "certain amount", but adding the first curse to a HP deck really hurts it).
6. Philosopher's stone (dropping 4 cards might push you up to 8 coin so why take the curse?).
7. An overpowered trade route (e.g. on a board with island, great hall, noble, and silk road) as this allows you to hit a province & save your other good cards.
8. Chancellor in chancellor/stash combo. You can buy the estate and your only real goal is hitting the stashes next turn.
9. Scout in a nobles/GH/harem deck/+buy deck.
10. Tribute against an opponents harem/nobles deck.
11. Native village.
12. Golem.
There are just a lot of decks that are reliable enough where the curse is much more painful than losing cards. Even without a way to chain back up, I can see a number of truly dead terminals that could benefit from discarding.