I find it interesting the biggest naysayers are from Alabama and California. Now I could be wrong and they could have just moved from a heavily moose populated state or are well off and have shot multiple moose on many guided hunts. Even so most trophy hunters aren't going to use something like a 243 so they wouldn't know how it would work in the first place. I would listen to the guys (Alaska, Canada, Sweden) that have a chance to shoot moose yearly and for the meat not just the horns.

I personally only know of one lady who used a 243 and 100 grain partition to shoot her moose. It happened to be the same moose she had shot in archery season but the arrow didn't penetrate the shoulder blade. The partition did though.

I think like has been stated the 6.5 would be a better choice and is a classic moose slayer without much more recoil. Or get some managed recoil loads from remington (I think) if you don't handload for the '06 and if you really don't feel comfortable with either the 243 or 6.5. That said I think with some heavy premium bullets in the 243 and a good shot through the lungs you will have your work cut out for you packing.