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I live in the North East which is a little better, but I have some rust of my rims ( 2009 V7). Have been trying to keep the rust at bay with chrome wax. So far it's worked ok aside from a few tiny bubbles.You could try one of those compounds that attack rust, like Evaporust, and then some steel wool and polish if you want to keep the chrome rims.
If I had the steel rims, I'd either get a newer set of the aluminum spoked rims from a Special or Racer. Or, the cast aluminum from the Stone.
My79 triumph has it's original chrome rims without a spot of rustI wipe them down with wd40 and coat with waxI live in the people's republic of Connecticut