Though I have never hunted Buffalo I have a friend who shot one a few years ago. Kind of like shooting a target at 100 yards for him. 140 gr from his .264 Win Mag., full broadside. One shot.

Not the medicine I would use, but I believe you already shoot a .340 wby. Big Bullets that stay together would be great medicine for the shot. Perhaps Barnes TSX at 250 gr or the 250 gr Accubond from Nosler.

The buffalo probably won't even twitch when he hits the ground.