If you research further you'll see the original 6.8 designers preferred slower twists and knew these twists would perform better. 1:10 twist barrel blanks were used initially due to being popularly available... as .270 Winchester.
Make sure to read the stickied 6.8 barrel testing reports above, and search the thread histories for topics such as DMR, SPC II, etc. There is tons of info on this forum if you have the time to read it.
Long story short... at a minimum you want the SPC II chamber, or DMR chamber, and twist rates of 1:10 at the fastest, and preferably 1:11, or 1:12. The industry has largely moved away from the ridiculous SAAMI chamber (thanks Remington), and many companies are moving to different twist rates or rifling types to further reduce pressure and increase performance.
For the hunting and shooting you mentioned, you have several good selections to choose from. The Xtreme 6.8 uppers, LWRC, Noveske, Stag, RRA, WOA, Denny's GTS, POF, Addax Tactical, CMMG.