I'm sorry man, but I'm doing the best I can with the knowledge and equipment I have.
I got the set for free, and I hate to spend a lot on equipment to get it working. You're right that I don't have a lot of experience with high voltage equipment. I have it just *almost* perfectly working, and there are just a few small problems I still have to work out, so I kind of just started trying things.
As for the alignment, I just kind of figured I'd try to do it by eye, and if that didn't work (which it didn't, as I shattered one of the cores when I tried to turn it), I'd pipe in composite video. That's what I'm doing now, and it's working great. The point where I tied the video in is at the grid of the video output tube, which is supposed to be a 1V Peak-to-Peak signal, and is DC biased at -0.5V, so the composite video signal is close enough to work, there. I have the audio going straight into the volume control, which DC biased at 0V, but I think it's expecting a higher signal amplitude, as the output is kind of quiet.
I can pick off the hot glue (I've done it on a lot of things before) and clean the HV cup, as you suggested, and see how that works. I do appreciate the advice, even if you have to give it harshly.