I walked into the LGS several months ago and bought an older (I estimate 15 to 20 years) integrally suppressed Remington 700 in 308. It was made by BGW in Gun Barrel City Tx. From what I can tell by putting a cleaning rod down the bore, it seems to have a 1 in 12 twist and a very short internal barrel 12" to 14". Unfortunately I can't find any tech specs on the gun and so far, haven't been able to disassemble it. Does anyone have any tips on coming up with a subsonic load for this gun? I'd like to shoot a max of 300 yards relatively accurately. I am assuming that I will need to stay with lighter projectiles so all the 180 grain and above stuff is out. I've also been looking toward Tightgroup and Red Dot as Trail Boss is unobtanium. I have been looking at teaming this up with a 168 grain SMK. The Hodgdon website has a load for this. I am concerned about finding a load that is stable in the gun as I can't exactly leave the can off in the beginning to see if it is keyholing.

Any tips, tricks, guidance, is much appreciated!

1050 ft per sec is probably going to be bullets in the over 200 gr weight class.
https://www.midwayusa.com/product/1001919172?pid=998404

Cheap 147-150gr projectiles and trailboss

Super quiet and no issues with 1:12

Trailboss is apparently not available these days. I've read that people are using tight group and red dot in it's place.

Any recommendation on what type of projectile/bullet?

If it is possible, I would prefer subsonic for this. My priority is really having a very quiet gun that I can plink with and be reasonably accurate. If that doesn't pan out, then I will just load normal ammo and shoot it.

Unique works too

i download IMR 4895 for my subsonic 308 , 13.5" barrel with a 10 twist.  i use 220gr berry's and 190gr sub-x bullets but you might be able to get a 175gr smk below 1050fps with it

i use 200gr lapua subsonic bullet's and trail boss for my target loads.  if trail boss or an alternative doesn't show up before i run out S&B makes a subsonic 308 load with the 200gr lapua bullets that's excellent.  the 200gr lapua's generally do good out of slower twist barrel's but i haven't tried them in anything slower than a 10 twist

sounds like an awesome rifle by the way

Unique works well with the 200 grain Makers REX.