You are wanting precision rifle accuracy out of a main battle rifle.
You are chasing your tail.
Even the vaunted PSG is not capable of the same accuracy of a dedicated precision rifle. No need to get the high dollar recoil buffer, just get the Buffer Technologies buffer for $15.00 or so.
Trigger work will help, YMMV with Springfield-he used to be great but I have had to rework a couple of his that were not so good. As of the last couple of years it seems his work has suffered. Check Williams for trigger work, http://www.williamstriggers.com/
Check the triple frame to barrel, if it is welded to the barrel forget it, you don't have a floating barrel so harmonics are of minimal value. I have seen both on a PTR and barrel wise the PTR barrels are heavier profiles, again minimizing harmonic issues.
One of the biggest detriments to accuracy on the HK platform is the mechanics of the locking system and the chamber flutes.
For optimum accuracy the bolt must go into battery and lock up the exact same way, every shot. Mechanical consistency. Due to "battle rifle"tolerances and the roller lock up this is virtually impossible to achieve. The flutes aid in case extraction by gas flowing back as the breech unlocks, essentially floating the case out of the chamber. Great for reliability but rotten for accuracy and it allows debris and carbon to blow back onto the bolt face, further hindering accuracy.
Not knocking the HK platform at all, my favorite MBR. Rock solid reliability, good accuracy and will eat any ammo you feed it.
Just not a precision rifle even in the PSG configuration, more of a DMR.