Interesting challenge! Its curious how programming leads to this systematic analysis and the revelation of complexity even for “simple” things
There are some games where the turn order can be influenced that I am not sure are covered by your rules:
5 tribes has a auction-style system by players committing a certain amount of currency to occupy a specific slot in the turn. For 2 player game each player goes twice and auctions twice for the upcoming turn
Bot factory is using a rotating worker placing mechanic with 4 sections with each 2-3 worker position, with the limitation that you cannot remain in the same section
Castles of Burgundy player order divided in 5 turns divided into 5 phases which changes depending on playing certain tiles (ships and specific monasteries)