The problem is that Large pistol primers are shorter than large rifle primers. When fired they tend to slam back into the breechface, often damaging it around the firing pin hole. This has been noted on modern rifles, the older steel in a trapdoor would be more problematic.
Large pistol primers can help with standard deviations, but mostly in smaller cases like 32-40 and 38-55. Once you get to the 70 grain calibers it's harder to see, especially if using compressed charges. Those that do use them often use some sort of spacer in the primer pocket to prevent the damage mentioned above.
In a Trapdoor I simply would not do this. Unless you're looking for single digit standard deviations in velocity to limit vertical stringing at 1000 yards, it's just not worth it.
This--LPP being shorter than LRP--is the problem. Over the years I've seen a number of trapdoors with damage to the breechface due to the use of pistol primers (and damaged 2 myself, more on that to follow). The damage caused is fairly consistent: the metal around the firing pin hole gets peened, creating a recess around the hole. Trapdoor breechblocks are case-hardened; the softer metal under the case moves on the impact of the primer.
Since the only place the metal can go is into the firing pin channel, eventually you get a situation where the firing pin is locked in place. If you are lucky, you have ignition problems. If you aren't lucky, the pin sticks forward during a timed-fire match so when you flip the breechblock closed on a new cartridge, it fires before the breechblock is locked in place.
At best, this guarantees that EVERYONE on the firing line is awake. Worst case. . . well, I've never heard of anyone dying, but when a trapdoor fires out of battery it can get messy. (On the bright side, this does sometimes create an opportunity to acquire a trapdoor at a really
really good price.)
I did some experiments with back around 2005, after seeing a gun fire out of battery due to this problem, and came to some tentative conclusions. "Tentative" because I just didn't have enough data points. (Over the course of about 2 years I burned up ~2,000 rounds and ruined 6 "orphan" breechblocks. I couldn't afford more at the time.) I basically took my "new" very cheap 1884 trapdoor and a selection of breechblocks and set up test loads with different primers.
The peening seemed to occur earlier with early (high arch) breechblocks. Using later (low arch) breechblocks, the damage would still occur. It just didn't seem to happen as fast.
Firing pins seemed to stick forward sooner when the breechblock used a firing pin spring. I think this is because the spring effectively reduces the diameter of the firing pin channel/increases the diameter of the firing pin. My impression was that the aluminum-bronze pins may be slightly more prone to sticking in damaged breechblocks if the gun is fired rapidly ("mad minute" rate of fire). I have a hunch this was due to the alloy expanding more/more rapidly.
Use of LPP with paper shims seemed to result in smaller standard deviations in velocity, but at a slightly reduced average velocity (ca. 20 fps). I could see no difference on the target, shooting from a bench out to 500 yards.
Damage occurred more rapidly when using LPP in smokeless loads. It happened in BP and duplex loads at about the same rate.
Looking at the OP's primers, I suspect the primer piercing will resume when full-power loads are fired. He might want to remove the breechblock from the rifle and put a straight-edge across the face to see if there has been any previous damage.