Almost forgot to answer the question at hand: What do I do with my coyotes after a kill?
Anything with mange is buzzard bait. I'd say late 90's through late 00's we went through a rough time with mange, it was pretty rare to pick up many without it for a long time. The last couple of years have cleaned up nicely in most of the areas I hunt, but we did run into a BAD spot in western OK last winter. 2 trucks took 52 dogs over 3 days (running hounds sun up to sun down), couldn't keep but 13 or 14 of them.
Anything during the summer (KS is open season year round), is usually buzzard bait unless I have a use for it myself.
Good winter primes, it depends what they're bringing. I put up most of my hides (fleshed, salted, stitched, and stretched), but there have been a few years where "county bounties" have been good enough for ears that I don't bother. I've also had years where a certain buyer will take full carcasses, or raw pelts for almost the same price as put-up hides, meaning less elbow grease and more sleep for me.
Sometimes, on a unique looking or really well primed dog, I'll skin them with the paw pads and toenails intact (PITA to do, pretty much have to skin each toe), and include the skull along with it (for the teeth), one of my buyers sells to a few taxi's and he'll fetch really good prices, so he'll dump another $50-75 on top of it. I skin all of my bobcats that way, unless they're kits, which I usually let walk anyway.
So yes, having 6+ dogs on the back of a wagon makes for a pretty dang long day. Guys work up their own way of doing things. Skinning a coyote doesn't take that long once you get practiced at it, at my best I've stripped 10 dogs in an hour (pouring sweat mind you). The sooner you get to them, the easier it is, when we're running hounds, we strip all of our coons in the creek as we go. Coyote calling is about volume, so we don't take the time to do it until the end of the day. 2 or 3 guys can strip down 6 fresh coyotes in less than 2 beers, er.... I mean, 30min...
That said, if we don't get to them for a few days, we let them freeze, then gotta thaw them out, and that hide is STUBBORN. Much much better to get it off while they're still warm.