I feel that the bowl of the P should be larger, to match with the low crossbars of other capitals and the roundness of the lowercase.

I agree. /R looks correct, but the bowl of /P should be larger. The bowls of /P and /R don't necessarily need to match, and in my opinion they should never be the exact same bowl because in case of /P you need to compensate for the large space underneath the bowl.

I also think the vertical serifs (E, F, L, T, Z, z) are too big and robust. It's not bad, but then I would make the other serifs and terminals more robust as well. You probably need a bit more consistency in your design.