The FPRP does need to have the gap facing upward toward 12:00, to avoid the firing pin impacting the gap when it is hammered forward or rebounding backward, but you shouldn't need to drive it out to confirm that... just shine a flashlight through there and you can see where the gap is. If it's not oriented correctly, sure, drive it out and re-install it.
However, as mentioned above, that doesn't sound like it would cause the FTE problem you are having. The way I understand it, if a firing pin problem, like a mangled stock FPRP sticking your firing pin forward, causes a feeding malfunction, it normally causes a failure-to-feed because the cartridge doesn't have clearance to get into the chamber in the first place... the rim runs into the protruding pin on it's way up the breech face. I guess that's preferable to the gun firing out-of-battery, going full-auto, or similar scary outcomes.
I never had a FTE with my P-07. The only failure-to-feed I have experienced was with one specific type of ammo and it was dragging against the bottom of the slide due to its shape and dimensions, but on a full mag only, so you stripping the mag would have solved that problem. Your problem does sound like a sticking issue for the round in the chamber, so as mentioned by others you should plunk test some of the rounds that it failed on. I would also inspect the chamber and throat of the barrel, visually, also maybe run a tight-fitting bronze brush through there a few times, followed by a few cloths on a tight-fitting jag, to see if you can feel it hanging up on any particular spot, and also to see if anything interesting comes out.
