In an ideal world, we would have the 6.5-06, 7mm-06 (not 280) and 30-06. Then the 308, 7mm-08 and 260. Today, it is what it is and there really are no gaps in the field. You ask about 6.5cm, but seem like your looking for a hunting round. You got to pick one, and the choice depends on what you need to supplement your 30-06. Lighter gun, more distance, less power. Or do you plan to shoot 500 to 1000 yards steel plates? The 30-06 was used for long range target shooting for many years.
IMHO, What made to 6.5x55 great was heavy bullets at very effective velocity. Only you know what matters to you. I get a lot of mileage out of the 7mm-08 but I dont live in Montana. I also have a 30-06, it is simply overkill for my hunting and you can guess from my moniker, if overkill is the goal, I will go much larger.
I will go out on a limb and wild a guess, you would be very happy with something like an excellent light weight Kimber or even a Rem Model 7, if they are any good these days, in 260. That is since you are interested in 264 bullets. The 7mm-08 is popular for good reason, negligible recoil in light guns. The 260 probably just a little less of the same.