the psl (also called the fpk and now sharf schuetzen gewehr 97...hmmm...a german abbreviation on a commie rifle??? go figure1) is NOT a sniping rifle...despite advertising claims to the contrary.
neither is it a dragunonv, as you realize (but others may not).
it is a reinforced kalashnikov, long-stroke gas system squad marksman rifle and is deployed to that end.
yes, 1-1/2"-2" is about the best you will get. vertical stringing, due to the long, thin bbl. and tighly fitted gas tube is to be expected as the pipe gets hot.
pressure on the forearm will also affect repeatability of the impact point.
lastly, the gas piston mass also upsets the balance of the rifle at shot release...or, at least has some influence on harmonics depending on which experts you subscribe to.
as an all-'round shooter, the psl is a fine, economical rifle. it is sturdy, easy to service and maintain and any kalashnikov user can pick it up an go with it. an m24, it is not.