RE: How does your club handle this?
Two of the clubs I fly at in Oz handle this same issue this way (Our MAAA dues are due at the end of June there)
"Any member who hasn't paid thier dues by 1/July is not allowed to fly until those dues are paid"
"Any member who pays their dues late can still re-join the club without repaying the nomination fee but if one year has elapsed, the nomination fee will apply".
In Oz - the clubs collect the entire membership and submit te return to the MAAA(aussie equivalent of the AMA) on the members behalf. for those of us that are members of more than one club, we just show the other clubs the receipt from the club where our MAAA dues have been paid and they don't charge us that part of the fees.