I have never had a slam-fire, but my understanding is that seating the primers well below flush goes a long way toward solving the problem. FWIW, I have used Winchester primers for thousands of rounds of M1 and M1A ammo without incident.
You would think deep seating primers would make a difference, and maybe it does, but it does not totally prevent slamfires.
Current wisdom used to be as long as the primers were seated below the case head, nothing was going to slamfire. I found out that current wisdom was all bunk.
My second slamfire, and one that blew the back of a Garand receiver off, was with Federal primers. The cases were sized in a Bonaza match die, but that die was not a small base die, and the cases were a little fat. I had reamed all the LC Match primer pockets to depth, and primed by hand, but the rifle still slamfired out of battery as I fired rounds from the clip.
It is my considered opinion that overly sensitive primers are the primary cause of slamfires. And anything that delays bolt closure, like over long, or "fat" cases, just increases the chance of an out of battery slamfire.
Federal primers are the most sensitive primer around. I will never use Federal primers in a M1a or a M1 Garand again. And I would never ever recommend them for a gas gun.
Federals shoot just great in bolt guns. For coil cutting types, Federals are often the only primer that will ignite in their guns. (And these types then blame the primer manufacturer's for their problems!)
What you want is the "least" sensitive primer. Unfortunately #34's are hard to find at times. In my experience CCI200 are less senstive than the brass finish Winchesters. I have never used Remington's.
The best primers were the old nickel plated WLR, but Winchester stopped making those in 1999.
