I just rebuilt the primary cylinder, as recommended. It was an easy job - the only thing that surprised me was the little metal shield inside the reservoir that covered the compensation port. I knocked it out without noticing and didn't know which way it went back in. But I found photos on this forum.
Sure enough, the compensation port was totally clogged, exactly as this forum said it would be. I cleared it with the wire from inside a twist tie, scrubbed everything with brake fluid and put it back together.
When I initially bled the primary, I couldn't get the fluid to flow until I used my finger to cover the outlet hole on the primary and keep air from getting sucked back in. Once I got the fluid moving I connected the hose, bled it again at the secondary, and everything worked.
The test ride was good but short, so I'll have to do a longer ride to tell me if the fix holds.
Thank you ST1100 owners!