So now my question is: What makes yours (and select others) connectivity flaky, and mine (and select others) not?

If I was having flaky service, I'd be as frustrated, if not more, as you. I did have flaky service, but was due to a bum PAP2T. It worked for about a week, then started randomly losing re-auth. One line, then the other, then both, then neither. It would change every 5 minutes. My wife was beyond frustrated and wanted to just get POTS. I'd spend every night for hours trying different things (routers, firmware, settings, etc).

I plugged in another PAP2T, and now it's solid.

Not saying it is your PAP2T, but maybe?