To answer your question about disposal...........see hunting/coyote hunting/carcass disposal,
on this site. I don't know how to post a link, or I would do that.
It is much better to leave the coyote where/near where they died, then polute our resources and aggrivate the public with gross display of carnage. My opinion is that the deer carcass dumping is just as much , if not more aggrivating to the public than the coyotes are; at least the coyotes still have their skin on!! Bambi without his skin is probably more abrasive to the general public than Wiley Coyote/Big Bad Wolf is. Regarldless, neither one belongs where whey were dumped at.
Coyote numbers need to be kept "in check" in alot of areas, not just where they are causing problems. If they are suddenly causing problems in one particular area, it's because they have over populated in another area and have expanded their territory.
People who are paid professionally to take coyotes don't/can't just take the animals where they are causing problems.............they have to take them in surrounding areas too (den pockets, pup raising areas, heavy traffic areas, prey migration/habitat areas, ect.) When I was hunting coyotes professionally, the landowners didn't want to see the coyotes (dead or alive)..........much less hanging on a fence or decomposing by a gate/road, or any other visible spot!!
A creek/river running under a bridge, on/under a public road has got to top the cake.? I would have taken the effort to scatter them in the brush, rather than make a public spectacle.