Now that we have a great UI for allowing people to close their own questions as duplicates, I think we should be able to offer that UI to people even if we are out of close votes.
Proposal: if out of close votes, if you click close, allow the user to choose the "duplicate" close reason. This will present the UI for users to close their own question unilaterally with the Community user.
Obviously, to prevent abuse, there would need to be some throttling on putting banners up for users. Perhaps, doing this would cost a flag?
What it should not do, of course, is actually put a close vote on the question. The question about whether this would put such questions in to the CV queue is one for a separate debate that we do not need to have in this question again