hmmmmmmmm you already have a great "woods gun" for deer sized game with your tutty-tutty. You likewise have a "decent" big game/non dangerous gun with your .308 even though it generally is accepted and recommended that you keep your shots under 300yds with the 308 if said game is larger than a caribou. (Which is partially why I am about to make the recommendation that I am, why spend the time and money on a elk hunt only to "limit" yourself too 300yds with the 308?)

I believe a SIMPLE caliber for the heavy stuff (at any ranges you choose) would be the ol warhorse 338 Win Mag. It aint purty, it aint a shortmag, it aint blazingly fast and it aint new. BUT it will still "get r dun" like few others and ammo costs are reasonable for a big mag. Rifle wise, pick your poison. There are few fewer bad rifles on the market today than good ones so whatever you like is what you should pick. Scopewise, I probably would stick with something simple like a 3x9x40 or 3x10x44 at the most! Leupold VXII, Nikon Monarch, Zeiss Conquest they will all get the job done and stand up too the belting a 338 can dish out.

That's my .01/2c,
RA