Okay, here's a big update post.
Of the problems I listed last time, several are now fixed.
I replaced the 8BU11 tube, which has the sync separator. Sure enough, the vertical is no longer collapsing when I change signals. Picture is much more stable.
I also figured out why there was so much interference in the video. My matching transformer had a broken lead. I swapped a new one and the picture has cleared up.
I had forgotten my DTV converter box can play video from USB, so I went ahead and added a clip to check the colors. I haven't done a full greyscale alignment or anything, but I was able to prove that the color and hue controls work, and get the display pretty close to what I'm looking for. So I'd say my color is working fine now, minus the adjustments I need to make.
There's a few outstanding issues. I've taken a video to show them:
https://youtu.be/5xGn8A43S5A
There's a lot of buzz in the audio. I can get it to come through clear enough to understand it, but even with fine tuning the buzz never goes away fully. Is there an adjustment I can try somewhere? Maybe in the audio IF?
I'm also noticing a slight ghosting issue, especially when the images are static. It's almost like there's a second image slightly to the side of the color one. I've read about a delay line issue causing that, but I'm not sure how severe that would look. Alternatively, could it be a convergence problem? I tried to showcase that in the video.
Also, what I didn't show on the video, and I can go back and try to find this, is that when my signal isn't tuned in quite right, I often end up with a good image that's only in black and white. I can reliably get the color image adjusting the tuning. This isn't something that happens regularly, it only happens if the signal isn't tuned in properly. Once I lock it in, it's rock solid. I don't know if that's normal or not, but I figured I'd check.