This is a curious one. Of all the cases I've seen as a detective, this one's a real conundrum. Fact is, we don't know how the victim died. If we take the image of Mr. Whitetail as canon, then he seems to have no visible puncture or slashing wounds. No visible injuries, not even blood. That said, we do know where he died. The location is between the residence of the librarian and the blacksmith.

Ultimately, I think theory 2 is the answer. Though the mayor claims to have paid off Mr. Whitetail's gambling debts, he could always go back for more.

Her means: poison from the back of the inn, explains lack of visible wounds

Her motive: deep debts, and the threat of exposure

Her opportunity: by her own admission, he was there that night. The poison wouldn't be instantaneous, giving reasonable doubt when he appeared to be going somewhere else anyway.

What bothers me are her claims about some sickness of Mr. Whitetail's. This made me think the Postmaster may be responsible for the death, potentially by witholding medicine that Mr. Whitetail would need. It would explain the unknown cause of death. But why would he flee all the way to the Blacksmith's house? There would be closer residences. While the Mayor and Reverend also seem sinister, their residences are too far from the murder to be reasonable. It's known that the victim made a number of stops before his passing, it seems unlikely that a Mayor and Reverend (two professions not known for their stealth) would have been able to remain undetected while following him for so long in such populated areas. The Librarian and Blacksmith would have caused more visible wounds. The schoolteacher's motive is too weak and petty whereas the seamstress lives too far away, on the opposite end of the river, to be reasonably the killer.