"I suspect a intake/exhaust ducting problem. I just don't know where to start. It just seems like it can never get enough air. Any ideas?
If this is the problem, it is most likely affecting the operation of the sail switch. There is an airflow sensor in the ducting path that closes when the blower is operating. If the blower stops, or the switch is not closed, the flame will go out. This is an obvious and necessary safety feature. It is called a sail switch because there is a "sail" or flat piece that catches the wind and actuates the switch. If you are correct, there is just barely enough breeze to maintain the switch. You can verify your theory by finding the switch and temporarily jumping it out. If the flame stays on, you have found the problem that the techs missed. Now you have to figure out how to fix it.