Update time! (With pictures)
After my previous posts about the popped primers I was contacted by the nice folks at Murray's who said they have a solution beyond just smoothing out bolt face. Since I'm all about trying new things and was offered a good deal on having them do the work (both their new idea and the bolt face modification), I shipped off my barreled receiver and bolt/carrier/firing pin to them.
I'm not an expert on what they did but in a nutshell it goes a little something like this:
Mr. Murray had done some research on certain .223 guns having issues with handling the hotter 5.56 rounds. Apparently the answer was to "open" the "throat" or "leade" of the barrel (the part in front of the chambered cartridge where the bullet itself rests) which then allowed more room for the gases to escape. (I apologize if I'm butchering the explanation as I only have a rudimentary knowledge of any of this).
Mr. Murray, Ben to his friends and customers, thought "if it works for .223/5.56 then it should also work for 7.62 in an SKS". Would opening up the throat a bit lead to a loss of accuracy? Maybe, but since the SKS isn't a tack-driver anyway it probably wouldn't be noticeable to any mere mortal.
This "throat mod" is the new, ultra-secret modification that Ben references in the post directly above this one. He'd only done a couple so I was part of the guinea pig group.
I can't show any pictures of the "throat mod" (was going to call it a "throat job" but didn't for obvious reasons) because I don't have a bore scope but I will show pics of the bolt face mod.
Before
After
So did it work?
Since we didn't do this test scientifically (we changed two things at the same time instead of one and test then the other and test) I can't tell you what made the biggest difference - the throat mod or the bolt face mod. What I can tell you is this - the first time I shot the gun I got through 5 rounds of Wolf Polyformance FMJ before the first failure to fire (light primer strikes) due to pieces of primer wedging into the firing pin channel (figured that part out later). In total I had about a 20% non-fire rate out of 50 rounds cycled.
After the mods I went out and shot 20 rounds: 10 rounds of Wolf Polyformance FMJ (on left) and 10 rounds of this cheap, corrosive ammo I picked up (on right):

Fired slow, fired fast and not one popped primer or light primer strike at all. The SKS shot through all 20 rounds like a champ and at 25 yards with the stock sights in a poorly lit range shooting at a small target all 20 rounds found their mark.
I'll let Ben explain the details better but it would seem that he's on to something with both the bolt face mod and the throat mod.