It's unfortunate American is such sticklers for this. I'm flying down to FL on WestJet in a few days, and with them the first checked bag is free provided it's under the weight limit. There is a special dispensation for golf clubs however: they can be checked as a second item for no charge.
If I need to check a second bag, I plan on adding the required bits to my kite bag to make it qualify as "Golf clubs", which their website defines as, "One bag with clubs, shoes and balls is accepted per guest."
So, that will be a putter and a wedge, my sandals, and exactly two golf balls. The rest is just padding.
If they ask, I can confidently say it's "Sporting equipment and golf clubs." without moral hazard.
Not directly applicable to your situation, but if the airlines want to screw us on technicalities, we can play that game too.