I wrote the mechanism as stepwise. I don't think the pH gradient is too large to form an aminal and have it extrude hydroxide.
I have searched for bona fide examples of proton transfers with four atoms. If anyone has one, I am interested.
Six, beta-ketoacids or acetate pyrolysis.
Five, sulfoxide, selenoxide, or amine oxide eliminations.
As I had thought about it was whether the attacking and leaving electrons could both bond to a proton. That is, how acute of an angle can one still have a hydrogen bond?