Dave:
Traffic is a problem. Overseeding is a killer when combined with traffic.
I don't know how many rounds you do, I don't know if you have cartpaths, and I don't know if your membership will stay off the grass when excessively wet. I don't know your soils, and I don't know your budget. I don't know if the reconstruction company was good, and I don't know if your superintendent is good.
I know that it ain't rocket science. Its common sense. And if members would take the TIME to really understand agronomy (I mean like an 8 hour course), alot of grief and MONEY would be saved.
Has your greens committee invested any time outside of their monthly huddles?
I'm sorry if this seems rude. I have been witnessing the lynching of a friend of mine for a transition that he neither wanted nor had the support to acheive properly.
It seems to me that you should have good grass by this July.
If you don't overseed it will be good all year, every year. Especially in South Florida.