You have the right idea in the 6mms. A 6 mm Remington A.I. using 87 grain V-Max's is the ticket. The 6mm Remington gives you a longer neck than the .243 and it helps extend your throat life. Even though both the .243, and to a lesser extent, the 6mm Remington are tough on throats.
Pard and I have shot dogs in S. Dakota for many years, started in the late 70's. Our guns were 6 BR, then 243 AI, 12 twists on all.
With over a dozen 243 AI's under our belt, I can tell you the following loads have worked so well it is hard to imagine the accuracy with speed, and we shot Hart 12 twists, 243 AI, turn neck, with zero freebore 28" length-29" we liked the untured blanks in Weighted McMillen BR stocks, rigs weighed 26-28 lbs and with a muzzle break, they kicked very, very little. You saw your hit on every shot.
Fire form: Rem 7/08 Brass, 47-47.5g of Win 760, CCI250, 70g Nosler, TNT, or Blitz king at 3700-3750
Formed Rem brass: 48-48.5g of Win 760, CCI 250, 70g, 3800-3850
Max load is 50.5g of Win 760, with the lot# of powder that we had and add a Win mag primer for 4030 fps, tiny bug holes for groups from 47.5-50.5g. Pard settled on a lot of 48.0g and I settled on 48.5g, and I never used a full length sizer with this combo.
Now, for a walk on the wild side, go with a 14Twist, 6 Rem AI, with zero freebore, 50.5g of Win 760 with a 70g Nosler in Rem brass at 4000 fps, and 41.5g in a formed load got us to 4100, bug hole groups. Every barrel is different, so please work up to these loads.
Today, I would carry a 6 BR, 6 XC, and 243 AI.
For a chuck rifle, the 6 AI with a 14Twist with the 70g Blitz kings would be my first choice in a zero freebore chamber. 70g Blitz king is more explosive than the 75g V max and the Blitz king is put on a Match grade jacket...worth the few extra pennies.