The .223 I have is a 1/8 twist but only has an 18" barrel. I currently use that rifle as a training gun to work on fundamentals at 100 and 200 yards.At those ranges, either of the 6.5CM or 308 would suffice. Since you do not handload, the 6.5CM "may" have the edge over a 308. I used the 308 or 7.62x51mm for years on the 1,000yd prone and Palma lines, and it is very capable with proper loads.
Even today, we train a few new LR shooters with fast twist 223/5.56 rifles using 75-80gr bullets all the way out to the 1,000yd line. They are great for wind training, low recoil, and allow for numerous more rounds down range at reduced costs and longer throat life.
It's a sporter barrel that is suppressor ready, currently waiting for one to get out of jail that I will be putting on that.