I understand your feelings on carrying a heavy rifle for elk.
Another cartridge that would work is the 338 RCM.
I just put together one this year. Stuck a 22" #2 lilja SS on an old tang safety M77 SA. Lengthened the mag box to 3.1". 225 accubond with 61 grs of RL-17 2750 fps. Have a CDS turret on a 2-7 VX-2. It shoots well to 500 m, the longest we can shoot at our range. I am very happy with this 7 1/4 lb package. Will be carrying it on my cow elk hunt in NM in just a few weeks.
pic of rifle with old barrel