How would you resolve this situation?

I was storytelling a game earlier where the final four were Lleech, Soldier, Host-Amnesic and Mayor. The town had discovered by that point who the lleech was and were host-hunting, but were struggling to identify between a perma-poisoned amne who had received confusing stuff all game and the mayor who was trusted but fundamentally inscrutable as to whether they were poisoned or not.

The demon didn’t want to kill in the night as they couldn’t kill the soldier and didn’t want to eliminate a host-candidate between amne/mayor as that would assure her loss by exposing the other as the host (I actually can’t recall how but town knew the soldier was sober/healthy and therefore not the host). Similarly, the town was wary to execute since a wrong execution assured their loss and there was no concrete way of knowing what was going on- I was giving the amne believable but inconsistent information so it was possible she wasn’t poisoned.

We had I think 2 day cycles of no death and I realised that I had no way of ensuring an end. The fiddler would have been a terrible choice as the demon was outed by that point, but I was totally unsure of what to do. Eventually town just executed the mayor and lost so all ended in due time.

But I’m curious, what would have been a more appropriate way of dealing with this scenario?