alosso: Your last proposal punishes quitters with a bad score - would this work if part of them wants to avoid a low average and if won't count when the minimum number has been played?
Well, since it is an average, a real average, all they have to do to avoid getting a low average would be to play bad in general :)
I am not suggesting it would replace the current best-of-X-rounds average as the qualifier for a new tier, it would only be a number that more accurately displays your level of play. Sure, sandbaggers could go out playing bad on purpose, but that would be pretty pointless.
There is other methods to handle the sandbagging problem than to prevent them from keeping a high average. All that is needed really is to have your real average open doors for you. The good clubs, the good tournaments. Set them aside for those who have proven themselves worthy. Ok, that sounded elitistic, but why not? Why should someone with an average of 94 be invited into a prize tournament? In real life, they wouldn't.
It is not uncommon though that a player that advance to a new tier feels that he does not belong there. If the real average was a part of the moving up equation, I think it would be more fair. Currently if I, in a year as Tour Master, play fifty 9 hole rounds with a score of 29 or 30 and 500 rounds with a score worse than 35, I might be promoted to Legend. I am not sure that is ideal.