This is a very helpful thread. I have two Mac IIfx boards with battery vomit. I have been gradually cleaning them up and have had similar damage and issues, especially with the death chime.
Today I was finally able to get one board to start up after I found a small broken trace on the back of the board on the line from Battery 1 to D6. Just like yours it will not shutdown. I've got voltage to UI18 (when on). I do take extensive voltage readings, on the shutdown circuit. On Q2, I am getting 0v on pin 1 (emitter), 0v on pin 2 (base) and 4.4v on pin 3 (collector - single bottom pin). The resistor associated with it I get 0v on both sides. I do have continuity. I'm still stumped on shutdown. Reading your comment about UE13 and UD13 was helpful. I will recheck that area.
Even with finally getting it to boot from the start up button (I have been jump starting both boards) I would immediately get the death chime. I will look into buying the ROMinator, maybe that will help. I will also check my ROM socket.
Also reading about your issues with the BlueSCSI is interesting. I just bought three kits and haven't had a chance to build them yet. I also have a Mac IIx that I recently finished.
Thanks again for the insight, I will continue to follow this thread.