Well, after a dinner and a beer, I continued the research and plugged what I considered to be a part number found on the cartridge into google and found a discussion where "Mary" was in a similar situation. As a response, someone posted another exploded diagram of all the parts and now I see that I must have missed the 971-680 screw that holds the retainer and the cartridge inside the pipe.
The relevant part of the diagram is above.
Two good things about the diagram: One, it shows what I missed. Two, it seems to be the exact type of faucet I got. And three, the cartridge part number is what I got at Ferguson's today, so I should be able to fix the faucet using the part.
I am too tired today (had an intense workout plus the plumbing work), and will finish the work tomorrow.
Wish me luck.
And yes, I expect to run out of bad puns with "pf" soon. But not too soon, mwahaha!