The PSG1 is a delayed roller design, so may have a slight advantage over gas guns when it comes to keeping bullets going at extreme ranges. I can tell you categorically the Fed. 308M 168gr. will NOT be up to the task from a gas gun at 1000 meteres (almost 1,100 yds.). They go subsonic at about 800yds, the bullet loses stability when it makes the trans-sonic transition and does the "kickin' chicken'". This is true of both the Federal 308GM and the military's M852 (which also uses the Sierra 168gr. MK).
The US military has come out with the M118LR (Long Range)which uses the 175gr Sierra MK bullet, but I still don't think this is a 1000m cartridge (especially in a gas gun)! Talon makes a similar load known as "White Feather" match, Federal makes it as 308GM2, and Black Hills makes them calling them simply 175gr. Match. All of these cartridges use the Sierra 175gr. MK bullet. These are the best long range loads I know of for the .308.
You could also go the Palma route (very long barrel and 155gr. bullet). These bullets start out very fast from these super long barrels and can provide sufficient velocity to keep up good accuracy at 1000 YDS.
At 1,000 meters a cartridge like the .300 Win. Mag is called for.
Regards! DaMan