Ok, updates to this now. I went through both the sound board and the video board. I found and repaired two issues: 1. - A cap and trace on the audio board had become severed from the rest of the trace. I patched that with a wire. 2. - The ground to the chassis cage on the underside of the video board had become cracked, so I re-soldered it. This corrected two issues: The sound is no longer crackling or distorted (no doubt due to the cap being re-connected), and the video is now sharp and clear with no further distortion or bouncing.
HOWEVER: after working well for five or so minutes, the brightness of the screen began to flicker, until it became a more consistent dark. You can see the image, and it is clear now, it just is quite dark. So, now I am left to try and figure out what is happening here. At least the audio issue is fixed, as is the flickering video. I tried cooling the video components to no avail. Does anyone know what circuitry could cause the darkening of the screen? One clue: there is less of a high-pitched squeal from the monitor when it is dim. The squeal is higher-pitched when it is brighter.
An additional note: DON'T forget to reconnect the video cable from the CRT to the video board! I did that by accident and saw a big whiff of smoke so I shut it off immediately. I thought I somehow fried the whole thing, and saw the disconnected cable. I reconnected it, and then started it up, and the monitor worked fine, save for the problem that remains. Just a good warning for someone else doing this in the future.