I think on PPCG you should be allowed to close your own challenges single handedly. It would allow people like me who realize too late that I have posted a bad challenge and want to close it fast. But you end up with an answer so removing is not a option. Would this work?
This already somewhat exists in the form of duplicate votes. If you vote to close your own question as a duplicate, the Community user will hammer it closed.
As for other close reasons, it's best to edit the challenge if it can be salvaged, or just let others close it otherwise.
Note also that if you catch the problem quickly enough, you can delete your challenge (even if you can't close it). The rules about deleting questions are based on how many answers they have and how many votes the answers have, not on how many close votes they have, so it's possible that one method will work when the other fails.