And now, re-reading the Sticky for Executive club here in this forum, I see the caveat about booking directly with BA to get an upgrade. I DID read that section earlier in my research, but I guess it didn't register. Or perhaps since I didn't see it confirmed anywhere on BA's website, it became airborne and left my brain. I'm STILL not clear after re-reading it about the possibility of a two-class upgrade.
I want to reiterate, though, that the majority of my conversation with this agent was about the fact that I understand and accept that they have rules and policies, and that they can set those as they see fit, but that when it's virtually impossible to find those policies on their website, how can they expect people to abide by them?.
It's just a very unpleasant way to begin my experience with Executive Club.