Yes -- petros (~pebble) is the man speaking; petra (~boulder) is the truth spoken. It's on the latter, not the former, upon which the church is built. It's about what is taught, not who is teaching (as we see in Galatians 1--"even if *we* or an angel from heaven..."). I believe not in a 'succession of popes/men,' but in a 'succession of truth,' i.e., the 'faith once delivered.'
I saw your longer response (thank you very much for taking the time to write that), but am headed out for a few hours with my oldest son. I look forward to responding thoughtfully, hopefully later tonight.