I have a whole lot of experience with a 308 subsonic but not in a 308 Win rather using a 300 Whisper with a Gemtech can.
To stabilize the heavier bullets at subsonic speeds you will need a fast twist I have 1:8 Lilja barrel but you might get by with a 9 twist with 200 to 220 gr.bullets.
Shot placement on game IS CRITICAL as there is no expansion.
I have read repeatedly about "bullet upset" in tissue but have yet to see it on deer. It usually icepicks through.
Make it a head shot , spine to drop it there or through the heart and plan to follow with no blood trail.
I have shot the 240 gr. Sierra HPBT through 4 fresh 2x4's and generally find the bullet unscathed except for grooves from the rifling.
Do use the suppressor on a full throttled 308 and 270 to reduce the sound and recoil- when you shoot supersonic through a suppressor you get the crack but difficult to pinpoint the direction of the shot and you can usually forego the earmuffs as the sound is not unpleasant.
Remember, the POI is usually quite a bit lower with a can on- mine usually 12 inches low
Hope it helps some and is not too off topic.
Gary