Hi Bigdad! I bet you're getting more answers than you expected, even if they are not very encouraging answers.
The idea that "it will just grow back" seems very depressing. At least it isn;'t killing the trees its on!
Perhaps you can find something that the Spanish moss needs and you can deprive it of, or see that it gets less of what it needs.
It gets both water and minerals from the air, not the tree.
If your region is only marginally wet enough for it, maybe increased air circulation would discourage it by letting it dry out.
I don't know whether it would like more light, or more shade, but pruning might let in more light.
Collecting minerals from air-borne dust and leaf fragments seems like a chancy way to survive. Maybe (purely guessing here) when you pull off as much of the "moss" by hand as you can, spraying the rest with pressurized water would remove its source of minerals.
Dr Dawg has to fertilize his to encourage it ... maybe you can starve yours to discourage it.
Edited to add:
I'll go from "guesses" to a "dumb guess". Do you have any enterprising scavengers like squirrels or other tree rats? MAYBE spraying a little diluted molasses on the moss would encourage squirrels to eat the darn stuff. (As long as they don't chew the bark under it.)
Too bad chickens and goats don't climb trees.
