I would not use the 6 mm on sheep and that is put out as my opinion, not as truth from on high. Here is why:
I shot an antelope at about 300 yards this year with a 243 and an 80 grain Ballistic Tip. The Ballistic tip is a very fast opening bullet, and even at that, the wound channel was not very wide.
The year before that, at very nearly the same distance, I shot two mule deer, the biggest field dressing at 130 pounds with a 7/08 and a Hornady Interlock. The wound channel was much wider, about 2 or 2 1/2 times as wide as the wound channel from the 243, plus the 7/08 had power enough to drive the bullet diagonally through the deer, ending up under the skin on the rump.
The second factor that enters my decison, is, having gutted a sheep or three, I discovered that sheep have what must be the largest paunch in the animal kingdom, with the possible exception of Fred C Royce.
What that difference in body sheep means is that on a quartering away shot that on a deer would mean shooting into the rear of the rib cage, on the sheep you are going to have to shoot through a very large paunch. I would be much more comfortable with the larger wound channel and that I have seen from 7/08 class cartridges and larger than the smaller wound channel and lesser penetration of 6 mm class cartridges. I can see where a larger cartridge would be a definite advantage given these facts. It too would drive through both shoulders, given that you were offered that shot.
Bear in mind, this hunt is from the sounds, a once in a lifetime hunt and that you aren't a gun writer experimenting with what might or could likely work, you are in a situation where you want to hedge every bet that you can.
As I said, just my observations.
Fred