It seems like the 5.56mm version will do most of what you want to do, honestly. It's a fine catridge for anything white-tail or smaller, if used accurately, and will kill many much larger animals if so required. The only issue that jumps to my mind is humane killing. A humane hunter only takes prey within a caliberXrange envelope that guarantees a clean, humane kill. In the field, that envelope is smaller than it is on the gun range, due to the variables of the wild. So with that in mind, you might prefer your 6.8 variant for deer (since it gives you more bullet and thus more leeway in terms of bullet placement). Similarly, the effective lethal range of either caliber might be much greater than the range at which you would take a game shot with that caliber, as a humane hunter. With hunting loads, either of these calibers might be accurate and lethal to 400 or even 500 yards from the bench, but you may make a decision for yourself that that means you'll only take up to 300 yard shots on deer, just for the animal's sake. Call it an extra MOA for buck fever, funny breezes, and the leftover sausage you had for breakfast. It's also worth remembering that for hunting purposes, there's no reason to hot-swap barrels. Set up the rifle for the game of the day and then sight it in and leave it fixed until the hunt is over. That removes at least one variable.
There's no denying that the AR platform can be made very accurate (else people would not spend money on stuff like 6.5 Grendel). We have yet to see if the more proprietary ACR platform has the same potential, but you only need 3 MOA to hunt deer out to 100 yards. The only people taking shots at live animals from distances that require sub-MOA rifles and individualized ballistics tables and whatnot are soldiers whose missions require it, and for whom a gut shot or near miss still has some positive tactical value.
Basically, what I'm getting at is that if you put in the work to find the right hunting loads (not mil-surplus FMJ, but proper, well-made softpoints) which perform well in your particular barrel and to become proficient with them, you should not need hesitate to hunt any of the animals you listed with an ACR in 6.8 OR .223, within the ranges you've found that you personally can guarantee the clean kill. And I'll bet that will be any reasonable range for such game, out to 300 yards if you choose barrel and ammo wisely. And you can kill a hell of a lot of animals in a hurry with a 10 or 20 round magazine. Take it pig hunting in Texas and bring home the whole family. Pork sausage from mama and a litter of piglets for the rotisserie.
The above presumes that 6.8mm SPC II kits eventually start to exist. Until they do, it's a good thing 5.56mm is viable, because that's all you've got in this rifle. Again, do your due diligence, but don't write off the 5.56mm as a perfectly lethal round for CXP-2 game and smaller.
The issue of Very Long Range shooting, 500+ yards, is even more vaporware dependent. Even for punching paper, you need a bullet with a decent ballistic coefficient and uniform shape, sufficient and (more importantly) consistent acceleration and muzzle velocity, and a fine-tuned platform from which to launch the missile. Whether it's 5.56, 6.5, 6.8, or some other cartridge, you're still talking about aftermarket barrels (with hand-picked profiles, rates of twist appropriate to the loads being fired' etc.), aftermarket receivers, bolts and carriers, triggers, and other components which exist in the AR market to support the precision competition game but which do not exist even theoretically for the ACR yet. Aside from a few companies doing SBR work, what Bushmaster is selling is what you get, and none of it is designed to win medals at 600 yards. Honestly, I doubt that anyone will try to take the ACR down that road. The ACR's design theory is one of ruggedness, reliability, and ergonomics (with a few small oversights) for an efficient tactical weapon. That may make it a very effective "dynamic game weapon," which phrase I just invented to describe animals taken at close and medium range, on the move, or under difficult hunting circumstances such as stalking and still-hunting. It does not lend itself to bench rest competition, though.
So, bottom line? What exists now is a 5.56mm rifle that will take game efficiently out to 100 yards, and further if it's small, weak game (varmints) and you do your homework in terms of load selection and practice. Oh, and it has all the benefits of being, y'know, an ACR. What is promised to exist in the next year or so is a 5.56mm and/or 6.8mm rifle that will efficiently take game or paper (as barrels in various twists and profiles become available) out to 300 yards potentially, again with due diligence on the part of the operator. A various-caliber rifle, capable of taking game to 400 yards and punching paper at 600 yards, may come to exist if the ACR takes off and Bushmaster makes it easy for aftermarket parts makers to offer elite variations on the ACR component menu. This last is unlikely.
P. S.: 6.5mm bullets are really cool. High sectional density, high ballistic coefficient, and enough popular interest to get the high end manufacturers interested in producing bullets in that caliber. That said, anything that uses a STANAG 4179 -sized magazine is going to be limited in its ultimate capabilities. Even fattened cases like the Grendel can only hold so much powder in that length limit, and fat cases with steep shoulders have additional accuracy and feeding concerns. Bear that in mind before you pour money into it.
P.P.S: Reviewing your original post, Murray, I would add that IF additional barrels become available in various profiles, for 6.8mm especially, then the ACR might make an excellent complement to your Mosin (which I presume is some kind of fairly long, fairly accurate 7.62 Russian Zaitsev-worthy Stalingrad Special). On a mixed-bag hunt, you would have the long gun as your primary large-game weapon, and you would have the ACR for opportunity targets scared up during a stalk or walk. If you are very confident in your carbine skills, you could even use the 6.8 version as a bear-defense gun, but be ready to put a lot of lead downrange in a hurry if you have a grizzly problem. I really do think that in the real world, you are unlikely to be able to shoot animals at 400 yards with an ACR reliably and humanely. However, taking as given that only the very rare and silly hunter shoots at an animal from farther than 300 yards (And besides, if you can't get within 300 yards of your prey, you aren't much of a hunter, are you--prairie dogs notwithstanding.), and presuming you can someday get a 6.8mm barrel of appropriate length, weight, and quality, then these two rifles should cover a wide spectrum of hunting scenarios. So maybe you don't have the 600 yard rodent headshot ready, but how common are those, really? Everything else, you're good to go. They would just look weird together, is all. Very "Odd Couple."
