`find`-like tool pruning most directories along a golden path

I have a directory tree whose overall structure is something like

logs/
  u1/
    p1/q1/r1/info
    p2/q2/info
  u2/
    p1/q1/r1/info
    p3/info
    p4/q4/r4/info
    p4/q4/r4/s4/info
  u3/
    p1/noninfo
    p2/q2/info

and I want to write a find invocation that e.g. returns all of the
info files contained in a p1/q1/r1 subdirectory while pruning as much of the search
exploration as possible (crucial given the large number of files).

So far I have

find -mindepth 2 -not -path "logs/*/p1*" -prune -o -wholename "*/p1/q1/r1/info" -print

where

• -not -path "logs/*/p1*" -prune ensures we prune off everything that does not start with p1
• -mindepth 2 ensures that e.g. logs/u1 is not pruned off by the previous predicate
• -wholename then is what I am really looking for

Although that already cuts the search space down by quite a bit, I’m still exploring a lot of subdirectories that are already doomed.

At a very high level, I basically want to be able to specify a regex for each successive directory nesting. Can I do that in find (or something similarly widely available; I don’t really get to dictate what’s installed on the box this will run on)?