You should tie that cat to the rocket and send it home!
Yikes, do you have a problem on your hands!
I totally get the living in a rural area, ain't nobody worryin' about a mess of cats at an abandoned house thing... I think you are on your own. Those cats are kitten machines, and there's plenty to live on in your neck of the woods, so they will keep breeding like crazy. You've got rabies and distemper to worry about, and a whole host of other cat diseases that could spread...
First thing you gotta work out is how to stop the population explosion, then you can work on decimating the cat pack in whatever humane fashion you think is appropriate. Here's one possibility, some stuff called feralstat:
http://www.communitycatsmd.org/feralstat.html
That will help stop the kitten crops. You put it out in food. Apparently some cat fanatic folks are concerned it could possibly cause diabetes and/or cancer... feral cats maybe should have more concerns with lead poisoning, seems like. I am always worrying about rabies and also about the plague, which is carried on fleas... You don't have to see too many sickly and dying cats or skunks to start getting nightmares about your kids/grandkids... I always find out the kids have found a litter of sick kittens and sick feral momma cat AFTER they've been playing with the sick kittens, which they usually find from the mewing, buried down in a stack of hay bales...
Rabies is huge concern. We even give rabies vaccines to the horses out here, because the horses (no kidding) get bitten by rabid critters and occasionally get rabies.
I don't mean to sound unsympathetic, but those cats are a health hazard... And this is coming from a person who owns cats and has adopted abandoned ones... You can try cage traps, but I wouldn't want to be handling any sickly, feral cats. But if you can get some of them turned in to the pound, all the better. Good luck