7-08 doesn't even have the performance that .308 has with the heaviest bullets. The BC is good but the case capacity isn't sufficient to use it.
The .260 and 6.5 suggestions are good for a short action, non-magnums because the bullets available for those size cartridges are a better match for that size case than the 7mm heavies are.
If you really want to reach out though, you're going to need a fast twist for the given diameter, and preferably a magnum (7WSM, 7 mag, 300 mag, 300 RUM, the various wildcats based on .338).
I always say:
#1 pick the target and use that to determine diameter
#2 pick the range and use that to determine how much capacity you'll need to get a bullet going fast enough to get there
#3 use those two things to find a caliber that is cost-effective and can do what you need it to do.
6.5, 7, and .30 will all do the same thing if the target is paper or steel, bigger diameters will have more recoil and use more powder, but ultimately, the longer, heavier bullets of larger diameter will have more supersonic range on the top end, and if underpowered, won't even have that.
The next challenge is that the highest performing calibers in any diameter will be hard on barrels, so you'll have to decide if that is worth it in the overall cost of shooting any given caliber.