Ask all the nominees to withdraw, then have a do-ever, no penalty, no foul. It's unlikely that all the nominees would immediately withdraw, but if a significant number did, I suspect the rest would see how ludicrous they looked and step down.
And if they did not, at the point at which withdrawals were deemed a crisis (50%?), the Hugo administrators would be justified in stepping in. Unprecedented problems call for unprecedented solutions.
Yes, this is an additional expense for Sasquan. But if the rumors I've heard of a recent surge in supporting memberships is accurate, the money is there. It's reasonable to expect that in a do-over, there would be a surge of memberships.
The "no foul" part of this proposal must be stressed if fandom is to heal rather than splinter. No one's broken any rules. If every nominee agrees to a do-over, there would be no reason to bear ill will toward any of them.
ETA: Yes, this is inspired by the withdrawals of Marko Kloos and Annie Bellet. I hate watching writers suffer, no matter what they've done, and in the case of Kloos and Bellet, their crime seems to have been being liked by people who wanted to see them win.