Welcome to the forum, zer0net.
Regarding the weird behavior when turning the power supply off, this appears to be a common problem. I've heard of it before. In addition, my 5020 does the same thing even though it operates just fine, otherwise. I haven't had time to look into it, but it seems like there's a very large capacitor on the power rail for the control board, perhaps to ensure that the pass transistors' gates don't suddenly open wide during power off. Nevertheless, it looks ridiculous (especially the final flashes of life at the end) and something I'd like to correct. However, the good news is that it is unrelated to the other problems you're having.
Nothing appears to be burned from what I could see in your high-res photos. The MOSFET gates on these supplies have been known to get damaged by overvoltage, though. So, that's one thing you might check by making sure the transistors still operate properly.
You might also start from the other end and verify that the potentiometers effect a change in voltage when they're operated. Also, check for cold solder joints between the pot pins and the PCB.
In your original post, you mentioned that there's no display. It appears to be working in your video, albeit showing all zeroes.