Thanks for the suggestions, everyone. I do handload, and I've tried the following primers:
Remington Small Rifle (don't immediately recall if they were 6-1/2 or 7-1/2)
Mild loads or near-max loads, 38 special or 357 magnum, all produce the same hiccups with primer flow in my particular rifle. Though, sometimes it's better or worse, depending on the load. Since my 44 magnum barrel works so well, I figured I'd just rechamber to something that uses large pistol primers, since they work well in my particular rifle. Also, since I'm using this on an SB1 shotgun frame, my rechamber options are somewhat limited. If I found a small primer that didn't flow so bad, I'd just keep the 357 magnum chambering and be happy.
I'll verify which Remington small primer I've tried, and if it wasn't the 7-1/2, I'll give those a try.
Has anyone used the CCI 41 military small rifle primers in their 357 Handi? I recall reading somewhere that these have the most robust cups.