My Striker has a 16" Broughton 8 twist barrel, and does .5-.75 MOA with the 115 DTAC bullet. I've also tried the 87 V-Max out of it, and couldn't get it to shoot, and the 100 gr. Speer BTSP, which would do .75 consistently. I did take a 565 yd. dog with it this year before switching to the DTAC, and it performed just fine. So far the only long shot i've had with the DTAC was a 680 yd. shot in a measured +/- 25 mph x-wind and was scant inches from the clump of grass we were shooting at for 1 shot. The WSSM needs a muzzle break if using a rifle scope as mine is.
My old 6.5-284 XP-100 was great for long-range varmints, and was responsible for several coyotes beyond 500 yds. and would be great with about any higher BC bullet 120 gr. and above.
The 22's with 69 gr. + bullets oughtta be good to 500 or 600 yds. stretching it. The bigger 75 A-Max out of say a 22-250 capacity should get u maybe 600+ on the good days.
The 6BR is gonna be about 200-300 fps less velocity than the 243, and u may be able to get to 500 yds. on coyotes stretching it IMO. My suggestion is to go with 243, 6mm Rem., or maybe the 243 WSSM, and be sure and put a 9 or 8 twist on it so u can shoot the 105-115's. 87 V-Max would be where i would start and go up from there. My WSSM gives me +/- 800 ft lbs of energy @ 500 yds with the 87 V-Max, and 100 Speer, and the 115 DTAC gives me more than 1000 @ 500.