300 or 338 would both be good choices.....or you could go between with the best of both???
.325 WSM? Flatter shooting than the .338 and with more umph than the .300.

If you are of sniper quality, and are willing to pass up the only opportunity you might get because of wind, obstructions etc., then following some others suggestions out to it's logical conclusion, you should get something like a .22-250? Head shoot them. All about bullet placement, is it not???

I too am a big fan of the Encore! In my group of hunting buddies we have accumulated, along with the ML, .204, .223, .25-06, 300 wm, and .325 WSM in rifle form and .204, 5.7x28mm,6.8mm SPC, and 7mm-08in the pistol setup. Nice barrels all.....and the same sweet trigger no matter the configuration.

Put you a Leupold onitand enjoy that Encore!!!