What the politics of Florida is, I will not address.
As for the yotes, the time to kill them is before they are a problem in killing calves.
That would mean thinning now, moving into the fall migration, breeding season, and denning to kill the pups and parents, then moving to their replacements.
In stating that, if you have yotes in a mated dominant pair who are not calf killers, they are eating something else. Dogs raised on deer eat deer. Dogs raised on birds eat birds. Dogs raised on fish eat fish etc... Cattlemen are quite content to have a dominant pair who eat calf poop, afterbirth and leave calves alone, while eating wildlife or pets. Understand that point, in you may take out a dominant pair, who is replaced by a pair where one of them was raised on calves or lambs, which displeases stockmen.
I have a family group here, with a big dog, who leave calves alone, but is h*ll on fawns and turkeys. I leave them to recreational trappers to thin the pups out, send the message there is danger here, and that settles things down. America really needs a sound wildlife policy but does not have one. High dollar coyotes with high dollar gas, is not thinning them out like in the 80's when people drove around hunting gamebirds. I had hoped the current administration would have legalized poisons again with application to stem the tide along with state and federal programs to take down the coyotes. In my region we have a big problem in wolves in Wisconsin, Minnesota, Colorado and Montana are pushing coyotes into western Minnesota and the Dakotas in numbers. I was talking to cattlemen in Montana and they can not get into the pens with cows anymore in wolf country, as they are nuts from being terrorized by wolves. Wolves are frequent predators in this area now.
As for getting into it, you can run ads in farm magazines, go visit local coffee shops, stop by livestock producers and tell them what you would like to do. You are going to have to bait the hole in showing you can catch yotes and solve problems, and then you might get paying jobs. In starting out, instead figure on the good will which will probably get you access to hunting and fishing which few else will have as your rewards.
Millionaire farmers are like everyone else in wanting something for nothing and they expect you to catch problems immediately and cheap while they pay plumbers and doctors 100 dollars an hour.
Hope some of that helps.