Cade, I have had a few of the exact same rifles you have. We hunted large deer in Nebraska and coyotes all over the West and Mexico with the 6 Rem.
For coyotes, we used a couple of different loads:
60g Sierra with 50g of Win 760, Win case, Fed 210 primer, seat the bullet to touch the lands if possible, 4000 fps and tiny groups. Work up a load starting at 49g and go up in .3g increments.
80g Sierra Bt Blitz, 42g of IMR 4064, fed 210, win case, 3500 fps. Mack Daddy coyote and chuck load, groups in the 3/8" area in a tuned rifle. You can get 3600 fps with accuracy using Superperformance powder as per my hunting buddy, I am sticking with IMR 4064.
85g Sierra BTHp, 38.5g of H4895, Win case, Fed 210, touch the lands, 3150 fps, not a hot load, very, very accurate.
85g Speer BTSP, Close to max load for the gun of IMR 4831, REm 9 1/2, touch the lands with the bullet, this is a deer bullet, NOT a varmint bullet, tougher than the 85g Sierra. Clobbered Ok large white tails.
85g non tipped tripple shock, start at 44.5g of R#19 and work up in .3g increments, Jump the bullet .050 from the lands, use a WLR primer, velocity will be 3450+. I shot a doe in the azz going away from me at 100 yards, broke a shoulder, bullet was under the hide on the right front shoulder.
95g Nosler parititon, Max load of IMR 4831, Rem 9 1/2, 3150 fps, 5/8" group, kills 260 lb white tails at 300 yards like an anvil fell on them, will completely penetrate frontal quartering shots, break shoulders, and exit rib cage on the off side, innards are shreaded...massive shock. Never shot a deer more than one shot with this load on large Kansas white tails to 350 yards. 95g partitions has been more accurate than 100g in my rifles.
A friend in Az hunted with the 105g Hornady BTHP with a hot load of IMR 4350 in his 700. I never tried this load but I saw him shoot it at the range. This is the load that I would use for longer range. He used this bullet on Mule deer and coyotes.
I am on my second 6 Rem reamer. I have the reamer cut with zero freebore than use a unithroater for desired length freebore. That long neck will hold a lot of bullet. No doubt in my mind that the long neck adds to barrel life vs a 243.