Ok guys, hard to believe - but I made it!! After burning the first IC, I managed to get everything up & running upon second attempt. And I only sacrificed 25% of my weekend to get there...
Now the screen nicely goes down when the Sony starts up, and goes up again when the projector stops cooling (not immediately after shut down - sigh!).
My only complaint is that the screen is rather slow. Behind the screen is a window, and behind the window (across the street) is the Embassy of the People's Republic of China, which therefore becomes illuminated by my projector for ca. 30 seconds before the screen is down... Let's see how long it takes until this gets me in trouble!
Here is the scheme of what I have done. I figured I better document this carefully, lest I do not know what to do when the thing stops working!