Just did some experimenting...
First, I stopped by the storage unit earlier today and picked up another LC--one which I last had on in November and had no problems with. It also has new caps, so it's in top shape.
When I got home, I plugged the monitor, as well as the same power cord and ADB chain, into the other LC, which was set up next to the one with the issue. No monitor problems!! (I refurbed that monitor myself and knew I had tightened the ground wire pretty well, so I was hoping it wasn't my doing!)
I plugged everything back into the original LC. The problems came back. I took the monitor off, opened up the LC, disconnected the PSU from the board, and plugged it back in. After all, I had just fixed an issue with the sound shorting out on this board (which is also re-capped). With the monitor still on the chair next to my desk, I tried it again. Success! If there was any interference, it was likely the product of my imagination.
I put the monitor back on the LC, returning it to its original location. Again, any noise lines were the product of my imagination or very, very faint. I suspect they'll go away completely, if they even existed, once I either move or replace the boards inside the monitor with the newly-recapped ones I have in the closet (I just don't feel like tearing apart a monitor unless I need to). I drew a little on Kid Pix and moved the pointer around a blank screen on a word processor. Again, I feel any lines I saw were a product of my imagination at this point--and if they were there, it's likely just typical CRT behavior that I've grown unaccustomed to after using LCDs as primary displays for the past 19 years.
My guess is that it was indeed an interference issue. Grounding or not, discharging everything seemed to do the trick. The speaker has been working well too.
I'm also happy I didn't have to donate a board from the other LC!
My other guesses? Some sort of buildup caused by the conditions around there. This seemed to start when I moved the LC to carpet temporarily while flipping a mattress in the same room. My guess is there was some static buildup when I moved it--but that's a shock to me because I move LCs all the time with the mobile lab.