I've been watching this thread for a few days, and it's sure taken an interesting turn...
When a shooter asks for a DRT round, I generally consider that he means he's wanting to recover the dogs, which in my mind, means he's a fur hunter, because why else would you be so concerned with easy recovery? Maybe I'm wrong in that assumption?
Personally, I can't find anything better than a .223rem for knocking coyotes in the dirt, especially at mid-range (0-500yrds +/-). Between 500-1000yrds, the right bullet selection between a .243WSSM and a 6.5-284 is critical (could throw many other rounds in that list as well, these are the two I use). BUT, these two rounds (or others in their class) are pretty dang nasty at moderate ranges, and you'll end up ruining good hides.
Now, if I want to blow a coyote in half, he'll sure be DRT, but I really won't care, because he won't be worth recovering.
So again, I'm confused....
To answer the questions at hand. Personally, if you can discern a significant difference in volume between a .223rem and a .204ruger, or even a .243win at half a mile, I'd buy you a drink. Sure, I'd say the .223rem is likely the quietest of the three, but is it significantly quiet enough that a .243 would bug the neighbors and a .223rem wouldn't? No, not at least in my experience.
Shot placement is key for any round. I've taken coyotes with my .30-06 and 150grn Winchester Ballistic Silvertips that I placed poorly and the dogs ran off, never to be recovered. I've also dropped dogs dead in their tracks with a Marlin 60 .22lr. Sure, a more powerful, more violently expanding round might buy you an extra few inches in poor shot placement to produce a DRT, but it's not a guarantee. Or maybe you're thinking that a more powerful round can cripple an animal so it won't escape, even poorly shot, but it's not humane, not good for hide hunting, and frankly, it's just plain nasty. I too have seen coyotes run with their guts dragging behind them from a poor shot, and I've seen a few coyotes dragging themselves away with paralyzed backlegs... Nothing that I'd want to be planning on.
The upper torso (chest cavity, everything forward of the diaphragm) is a pretty dang big target. Sure, sometimes a dog is running and you know you can't guarantee a "vital hit", but in my experience, those shots are the exception, not the rule.
The 6.8SPC is actually a very effective moderate range (0-500yrd) coyote rifle. The moderate velocities keep it from doing extensive pelt damage (more than a .223, but significantly less than a .243 in my experience). It basically bridges the gap between the 22cals and the .243 in energy, and being south of 3000fps helps keep hide damage down.
My night hunting rifles a .223rem and a 6.8SPCII AR, my short range/urban night hunting rifle is a rimfire (.22lr, .22WMR, or .17HMR). Frankly, if I'm a half mile or more from a house, I don't even bother worrying about volume.
When you're talking about fox, or $200-400 bobcats, I cringe even thinking about the .223rem sometimes, and would favor a .17Rem, .22hornet, or a rimfire, unless we're talking about long enough ranges to take some zip off of the .223 (300-500yrds). I am dying to get my hands on a .17rem for bobcats...