Have you considered a 300 win mag throated for the 200gr+ bullets? The article I link below has good info on both the 308 and the 300 win mag. The 300 win is near the bottom of the page. The gist is, a 190gr match load from a 22" barrel does not lose much too much velocity over the 26" tubes. I know I said 200+ but even some of the 180gr bullets from a win mag can hammer elk, so even a standard throated 300 win suppressed would most likely be pretty nice. The 300 win mag is relatively forgiving to load for a magnum.

http://www.tacticaloperations.com/SWATbarrel/

Gary