You'll be fine running a 140gr hunting bullet at 2600+. In my experience, albeit fairly limited, bergers are not the best hunting bullet in lighter cartridges. Yes they shoot great and have high bc's but don't necessarily perform well in all circumstances.
I have killed 3 animals with my 260rem that I had built last year. First was an elk. I'll probably never shoot one again with it. He stood there and soaked up 2 shots at 65 yards. Third shot I broke his neck.
Second animal was a Corsican ram on a Texas ranch hunt. He was facing me and I hit him just a hair right of dead center in his chest. He crumpled only to get up 5 seconds later. He stood broadside and then I hit him somewhere just below the spine. He ran off into the brush never to be seen again. Tracked the poor creature for 600 yards through the cactus and brush, (an experience I hope to never relive).
Third was a Texas Dall. 35 yards broadside. Center punched thru both shoulders. I wasn't gonna make a 500 dollar mistake twice.
Bergers are super destructive out of my 300wm though. I'll never shoot anything smaller than an elk with it unless I absolutely have to. Almost tore my muley buck in half last year.
I'm gonna side with WildRose and say just use a good, accurate, hunting bullet and send it.