exactamundo.
I have a factory parked P and I also do my own parkerizing. When I do it, I can get a thicker layer of zinc on there but the factory job is just fine. I haven't felt the need to repark my P receiver even though it is pretty easy for me to do it.
After I parkerize something, I mix up some goop to soak into it. I take some thick grease, beezwax, and some kroil oil and melt it all together with a bit of solvent. slather that into the park and let it soak in for a day then wipe off the excess. You could also slather it in cosmo, but I find it stays sticky whereas my mix drys nice so your fingers don't feel tacky. I've never tried baking in cosmoline but I bet that would work well.
Think of parkerizing like a cast iron fry pan. It needs oil to soak into it and polymerize. Always clean it with more oil and wipe off the excess. Never degrease parkerizing with strong solvents, or if you do make sure it gets oil or grease rubbed back into it. It is a porous coating that becomes durable because of oily substances soaked into it.