I've participated in many a moose kill with everything from 243 on up and I agree with John.......put one shot behind the shoulder into the lungs and wait a minute for him to drop. This can be done from a frontal angle also.
No shoulder breaking for me and I've had poor results from neck shots......the neck being a huge muscle mass on an old bull......two 180 TSX from 300 WSM didn't exit nor drop the bull as the spine wasn't hit.
I've reviewed video of 16 moose kills our party filmed and I find no noticeable effect from a second shot after a bull has been lung shot with the first round.

Last year, I gave my buddies 16 YO daughter a shortened 700 in 270 and some 130NP ammo. A quick anatomy lesson on where to hit em and she was off on her first moose hunt. She tucked one 130NP inside the shoulder on first shot and the bull collapsed within 20 seconds. Sixty-one incher!

So yes....your 7-08 will do just fine.

Someone on this site said "It ain't the arrow....it's the Indian".......