Tim I think its an excellent idea. With a couple of concerns:

1. Time. Sheep hunts take a long time. Moose hunts can take awhile. The combo would take a minimum of two weeks. Three weeks would be better.

2. Seasons. I'm not certain where you will be hunting. But, generally the sheep hunting is best before the moose hunting is good.

A combo hunt of Sheep/Moose and caribou would be an excellent combo.

Your 338 is an excellent choice for both species. Your 30-06 would work as well. I would suggest that you take both rifles, provided that you can take the weight restrictions with both weapons. I would guess that you will carry the 338 the whole time, but if something happened the insurance of another gun in camp would be nice. My 338 still has the iron sights on it. Some friends say that they look ugly. I can assure you, that if I'm in the mountains on a shale slide and the scope takes the worst of a fall, those iron sights could very well save my hunt.

Some will say that the 338 is "too much gun" for the sheep. But, I say take as much gun as you can handle profeciently. If you can anchor your sheep by taking out both shoulders and lungs it might save you from climbing down a dangerous cliff to recover your sheep. Sheep are bigger and tougher than some folks give them credit for. Dead is dead; use enough gun!