Your three gun battery of hunting cartridges is a great one: 6.5 CM, 338 WM, 375 Ruger. I personally thought you were well covered with the original two as long as you’re comfortable and proficient shooting both 250 and 300 gr out of the 375. A 250 gr 375’s trajectory isn’t too dissimilar from a 180 gr 30-06. Can’t think of anything a 30-06 does better than a 375. Certainly less overlap with a 6.5 CM and a 375 than any over the other alternatives posters have suggested.
I’m weaning my hunting cartridges as well. I’ve gone to 6.5 PRC and 300 PRC bolt actions for NA big game and have ordered a Blaser R8 with 223, 6.5 PRC, and 375 H&H for travel and everything else. My plains/DG combo will be 6.5 PRC/375 H&H and I’ll either take my 300 bolt action or add barrel for the R8 if I go somewhere 6.5 isn’t legal on plains game. Could also just hunt with the 375 on everything of course.
Again, I really like your two gun hunting battery in 6.5 CM and 375 Ruger. Others may prefer other cartridges or combinations for various reasons, but you’re covered from coyotes to elephant with those two. Plus, 6.5 CM is one of the most popular cartridges around so ammo is widely available and in a variety of bullet weights and constructions so it’s a great light rifle. Adding the a 338 WM for a long range hammer and you’re definitely covered. Enjoy!