SOLVED!
After doing some more research, I came across camcorder repair videos on YouTube by 12voltvids, a former Sony repair technician and videographer. He said that Sony camcorders in the late 90s and early 2000s suffered from corrosion within the video head edge connectors, and that the "fix" is to remove them and reseat them. He stated the same in multiple camcorder repairs, including this one:
https://www.youtube.com/watch?v=YJ4OQQUjVf4
Sure enough, disassembling the camera shell and doing just that completely eliminated the stripes in the video. The service manual for most of these cameras is available online, and disassembly isn't bad if you are at all good with a small screwdriver. One of the easier repairs I've done in a while. I've since transferred almost 60 minutes of footage to my PC and haven't seen a single issue with the video or audio.
Passing this info along so others can save their camcorders instead of trashing them for a very easy to fix issue.