I have 223s, 6BRs, a 6 dasher, a couple 6.5x47 and currently two 6.5x284(on my 12th? Barrel). No question the 6BR is going to be the winner at 300. At 500 the Dasher may edge it out. I have to get past 600 yards for the 6.5x 47L to be inside my 6BRs and the BRs don't take me out of the black from a sling. 6.5x284 is relegated to 1k and only when it's windy or I'm shooting a regional or championship. If it's calm~ish the 47L, Dasher or BR get brought to the line. Or a Palma rifle.
I'm curious about the details of your 6BR not shooting well. I've done three and all one them were ridiculously easy to shoot in the .3s from a rest. Even with round forearms.
for 600 and in you could build a specialty 233. 6.5 twist 32" throated for 90s but it's probably gonna be a picky bitch where 99.9% of all the 6BRs will shoot 29.5gr Varget under a 107SMK with a 450M sub half MOA all day long. Well, at least to 80-100 rounds.