Almost every "expert" hunter I've come across reports Elk are a tougher animal than a moose.
Plus, the vitals of a moose are like the size of a beachball.
I've taken 2 up here in Alaska so far. 338RCM for both. The rifle and cartridge are amazing, but your assessment is correct... Limited by ammo. I used 200gr SST factory loads.
My big moose was a charging shoulder shot, bullet fragmented, then a double lung as it cut to my left. The double lung looked like someone threw a supercharged baseball through its chest... What you would expect from a weaker lead bullet that expands massively.
Second moose was 1 shot in the chest, facing me, at 10 yards. Found the jacket in the rear quarter, lead stripped itself off, hopefully through the vitals and not meat as I'm still eating it haha.
So for me, I love the RCM, but it's not ideal with SST.
Go 30-06. Plenty of rifle, and you report it's accurate for long shots.