I did a ton of testing including drilling out the flash holes, using Magnum rifle primers, fast pistol powders as well as trailboss/tinstar ... etc. The best results were with Trailboss/VV Tinstar and pistol primers.
For my AI AT Covert and 20" barrels - Both 1:10 twist I found that I could use 190 - 200 gr match bullets (Sierra) and 11.0gr - 12.3gr of Trailboss or Tinstar (depending on bullet selection). I tried the 208gr AMAX which worked but was on the ragged edge of stability and results where not as consistent. COL = 2.800"
Primer selection is CRITICAL you have to test but I found that pistol and magnum pistol primers to give the best results - I like Federal 150 and 155's. I found one load with 190 SMK bullets using the components listed above that shoots 1/2 MOA (1" 5-shots groups at 200 yards) though the suppressor. Target velocity was 1,030 - 1,050 fps.
Note the factory Lapua .308 Subsonic ammo shoots 1 MOA at 100 yards in my rifle - good stuff. This uses a dedicated bullet designed for sub-sonic loading that would be a good candidate if you can get your hands on some.
220 RN bullets work really well with 12.3-13.0gr of Trailboss.
Note I shoot at 5,000 ft density alt. YMMV - good luck!
With subsonic ammo start high and work your way low ...