My choice would be a single shot s/s synt TC Pro Hunter in 300 WM with a 28" fluted barrel and with an overall length less than the Tikka T3 Lite with a 24" barrel, also in 300 WM.
I would also consider a 338 in the Pro Hunter but I would always recommend anyone considering this caliber for the first time, to test the recoil first. A lot of shooters find the recoil a bit high.
The stock design on the Pro Hunter is such that the felt recoil is considerably reduced - around 43% claimed.
The single shot feature is not really a handicap - I've never had to take a second shot on a large game but if you have to, you can reload the Pro Hunter very quickly using a cartridge saddle on the butt stock, etc.
I have owned a wide range of 300 WM including Sakos, Tikkas, Remingtons, Brownings, Winchesters, etc, but my favorite ones have been the Pro Hunter and the Tikka T3 for moose hunting. For a repeater, I prefer one with a DM for convenience.
My 2 cents,
Duke1
PS. The 35 Whelen is also an excellent big game caliber but I would not put it on par with either the 300 WM or 338 not to mention the difficulty in buying ammo for it. This is my favorite caliber for heavy bush hunting for deer where I use 250 gr or 200 gr bullets.