I started out doing long range shooting (600 - 1000m) with a .308 custom rifle on a K98 action with a heavy 24 inch barrel. That worked very well for me for many years. Then I took a look down the rabbit hole and ended up falling in. In no time at all I had a custom build rifle in 6.5 x 55 that i was pushing out to 1200m. That was replaced in under 2 years by a 6.5 Creedmore. This rifle is amazing and I have won many competitions with it. But at the end of the day, out to 800m, I am hard pressed to tell the difference between all 3. Out at 1000m, both the 6.5's outshine the .308, and I have proven this to myself many times over. At 1000 to 1200m the day depends on which of the 6.5's performs better. I for one would not bet 5c on the one being better than the other.
Or just say stuff it all and get a 7mm rem mag. That at least cuts holes in 10mm mild steel hanging plates at 800m, which is very impressive in anyone's books.