pump the brakes a bit, the .308 DOES have the "horsepower to go past 1000 yards and make hits." although I have not personally done it, plenty of people have. and those that have shot way out there, they are usually running some sort of adjustable rings/base setup like an ivey. the guys in "precision shooting at 1000 yards" (craig slack and bruce artus) had essentially home made ring/base combination to be able to hit out that far. and if I'm not mistaken, a 220 grain bullet from that .308 was recovered and it was banana peeled. so, I would say that if it has enough velocity to banana peel that bullet, it has enough horsepower for.........
No offense but the "I personally have not done it" comment above is not helping with this topic. The OP was asking for real world feedback. I have shot a mile and beyond and it was certainly not with a .308.
It's all done at 1,000 and 1,250 is a stretch. Yes, people have done it, however, its far and few between and in ideal conditions. Those that shoot ELR choose a far better BC/caliber.
I have many .308's and love them. I just know their limitations.