Hi and sorry for the delay.. I havent been on much lately..
I think you need to focus on the MPU board for now as the 01a-leds test should run forever without problems.. both LEDs should stay alternating. Also, the blanking test should be consistent as well. The resistor and LED setup you have is sufficient and it should always have the same result upon power up. The flickering should not happen there. You can run both of those tests without the driver board and still be fine.
I think the problem is that the CPU chip appears to be crashing and restarting. This could be because of insufficient power getting to the chip, or bad connections etc. Since you have gone over the board many times for cracked joints etc you should check for clean and sufficient power going into the board.
Once you know you have good power, you will need to verify the reset circuit on the MPU board. When the CPU crashes (stops processing instructions) it doesnt automatically reboot itself. The reset circuit is supposed to hold the reset pin low for about the first 0.5 seconds after power up. This is to give the rest of the circuitry time to get clean power and be ready. After this small delay the reset circuit completes its job and allows the pull up resistor (tied to the reset line) to pull up the reset signal to a logic 1. This causes the CPU to boot and start executing code.
You can remove your resistor-LED test circuit from the blanking signal and put it on the reset signal. I believe there is a test point on the MPU board you can connect to. There may even be one on the 40 pin connector. I don't have the schematics in front of me at the moment. You should see the LED come on about 0.5 seconds after you power up and STAY on.
Unfortunately, you probably wont be able to tell if the circuit is "flickering" in this way because it could be happening faster than you can see with an LED. Once you get your logic probe you can set it to "mem" sometime after the half second and the LED on it should stay out.
As for driver board lock ups, its not always the PIA.. sometimes its the logic chips associated with it, but let's focus on getting the MPU board reliable first..