Quite simply, the system will always be abused and broken as long as Tier is solely calculated on average.
Stroke play average is fine for placing people into stroke tourneys, but it is irrelevent for matchplay.
What if we had a separate ranking system for matchplay?
We will call it the "Club" ranking. It should be similar to rankings for chess. You Start at a base number. When your win rating goes up, lose rating goes down - but you get more points for beating a player ranked higher than you. you lose more for getting beat by lower level players.
Players with a high Club ranking get moved up in tees just for matchplay. SO that Pro Sandbagger would be somewhat reluctant to go up against a high ranked opponent as it would cause them to be moved up. Once you move up, you can't be moved back down, just like how it works for stroke play.
The bet itself could be used as a multiplier, but i don't know if that would be necessary.
Someone could be a Pro, but be a Club Legend. It's analogous to some local guy that plays 1 or 2 courses extremely well, and likes to hustle Matchplay - even pros should be wary of this character.