Yes, I know, that's a lot of quoted material to read through before wading into more thoughts but I think it's important to try to put some perspective into a request such as this. There's some good information in all of them.
Opinions are great, we all have them and they are appreciated by the members and posters. The drawback is that without experience or backup data, they are just that, an opinion. And in a situation such as this, the OP is looking at a significant investment when the potential of a less than stellar performance and disappointment is a distinct possibility.
The .308 Win. is one of my favorite cartridges if for nothing else, the flexibility it brings to many of the shooting venues. It's easy on barrels and there are a bunch of combinations of bullets and powders available from experienced shooters. But...
Weight it down with a heavy for caliber bullet (210, 215) and one powder (Varget) then expect it to perform admirably and consistently out to 1,300 yards, you are looking at a sackful of compromise where nothing real good will come of it except mediocrity. Not many of us find mediocrity acceptable.
I admit that I am not a fan of Varget. I gave all mine away a long time ago and never bought any more. There are better powders
for the shooting I do. Others disagree and that's their right.
1,300 yards should necessarily require horsepower and just because you want to reuse a short action, should not cause you any pain. Wind is the demon you have to battle once a bullet leaves your barrel. Between 0 and 1,300 yards, there is a huge potential that it will have a detrimental effect on each and every shot you fire. But those effects will not be consistent since the wind does as it pleases whenever it wants. If you're going to go into battle with the wind you need two things at a minimum; horsepower and BC.
I use the 6.5mm caliber frequently because of the number of fine cartridges available. Coupled with that, there is a huge selection of high quality bullets for longer range shooting. If you limit the bolt face to that of the .308 Win. then I suggest the 6.5 Creedmoor, hands down. Add one of the 140 grain Bergers over Re-16/17 and enjoy!

I shoot a 130 gr. VLD which is better number-wise than the 140's. Real performance though can be achieved by loading the 121 grain Warner Flat Line. Yes I know, they cost more money and you're really not competing anyway so why buy expensive bullets? Because they work for the situation you specify!
If you want to go for all the gusto, have your bolt face opened up and chamber for the 6.5 SAUM or the 6.5 PRC. Now you're firing on all 8 cylinders!
Enjoy!