Paul,
I know there are a ton of published studies where quail nests were observed. You may have found these already. Many are from TX by folks like Dale Rollins and the like, but others I remember were conducted in GA/FL areas. I would be they are old enough now they would be free source publications.
If you found them already great, if not, try google scholar for a cheap easy way to search by subject/author/etc...
I believe that most of them pointed fingers as snoe mentions at the mesocarnivores of smaller size, raccoon, opossum, skunk, though of course, coyote, feral hog and others including snakes take their fair share.
Many of these were done using cameras observing nests, others observed what the nest looked like after predation and took clues and sign into account.
The cool thing I remember from one TX study was about quail nesting in prickly pear cactus which essentially worked as a fence!
Wildlife society bulletin has quite a few, as would journal of wildlife management (JWM)
(In relation to the adult bucks killed snoe, I'd want to know the deer were definitely killed by coyote (ie. not wounded, wore out from the rut, etc...) before thinking they are taking too many. While of course they can take down big game and do readily especially in groups, when you look at carcass signs
and have a fresh kill you can really see how many other things play in to these events.
Having spent years with sheep, cattle, deer and others where coyotes were always thought to blame and had to verify, there are plenty of other factors that play in either to cause the mortality or at least aid in the kill.)
Back on topic though, do they not allow doe hunting on this club, I would agree the best easiest way to manage your deer herd, they could even do a youth hunt or something if the "men" don't want to kill does.
Justin