Never mind... just called VX to clear it up.

They said that all MCS and F customers are welcome to use priority screening lines (where they exist), and that's why the BP has "Priority" on it (separate from Boarding Group A). The postings in this thread before mine dealt only with VX pax in F, not MCS, so I had nothing to go on before calling. And as I said, I was caught completely off-guard by the hundreds of people all trying to get through Concourse A security at that hour, and even the 2 screeners who checked my BP didn't say anything about qualifying to use a different line.

This was my first VX flight and now I know. And now others reading the thread know that their MCS boarding pass entitles them to ask for priority access.