Breech face issue.
Quite possibly. (Although I don't understand why FMJ would work and JHP would not.)
In any case, here's some good news, finally.
I did two things: I rounded off the edge of the frame just below the barrel's feed ramp, using a dowel wrapped in fine emery paper. I also stoned the breechface, based on C&C's suggestion. One or both of those seems to have had the desired effect. I put about 6 mags of JHP through the gun yesterday, with zero malfunctions. Hallefrickinlullah! I just may have a gun that I can carry for self-defense now! I'll shoot it a lot more before I trust my life to it, of course, but this is a very promising result.
Side note: to do the testing, I bought two 50-round boxes of 115-grain JHP at Cabela's a couple weeks ago: one Federal (ACTUALLY REMINGTON UMC
), one W-W white box. The Federal has big muzzle flash; the W-W has none. It appears that the W-W has flash retardant added to the charge. Good to know if you are shopping, and you see them side-by-side at about the same price (which these were).
Thank you all for your suggestions.
EDIT: REMINGTON UMC, NOT FEDERAL