I think our original poster needs some encouragement.
OP, You already have a good fast, light, fairly flat shooting cartridge. Wonderful for smaller big game and adequate for elk and moose. If you want something that is actually different, consider a cartridge that delivers a substantially heavier/stronger constructed bullet at enough velocity to serve well at "normal" hunting ranges. (That means under 300 yards). The two cartridges I have used and liked for that application are the .35 Whelen / 250 grain bullets and the 9.3x62 / 285 grain bullets. Both are noticeably more effective on moose and elk if heavy bone is hit ( like the humerus/scapula joint ) and give very good penetration on rear angle shots if necessary in the bush. Both are quite manageable and appear to recoil less than a .338 Win Mag. or even some lightweight .300 magnums. Both seem to kill as well as the .375H&H which is also a classic choice, but getting into the "larger than necessary" category. Bot the .35 W and 9.3x62 can be found in rifles with normal action length, standard weight, and normal 22" barrel lengths, unlike many magnum cartridges.