OK, so I finally got some more time to analyze this problem.
My project is saved with SOLO and DIM buttons on. Everytime I open the project, the drums are out of sync. Not only out of sync, but playing at a slower tempo than the rest of the project, by about 20 bpm. Turning SOLO or DIM on and off while project is playing does not correct it. Sometimes, but not always, stopping playback and starting again corrects it. Turning PDC on or off during playback corrects it everytime, but it doesn't seem to matter if PDC remains on or off, drums still in sync.
After correcting it, I can make it happen again by stopping playback, turning DIM on, then SOLO. This sequence makes the problem return everytime.
Trying to follow the notes displayed in drum pane as the song is playing with the problem active, it seems that AD is playing midi notes that aren't there at all, and only playing some notes that are there.
A weird problem, but not too bad, I can still work around it.