Worn CRT or other issue? (Sony)

[grossbard]

I recently picked up a Sony KV-20V50 mfg in 1993. The picture had a red bias/tint/whatever you want to call it. I messed with the gain/cutoffs in the service menu and got it to look a little better. The overall image is still fairly sharp, but there's a bit of horizontal smearing.

I went over the power supply board and main board with an ESR meter and found several caps with high ESR. I replaced those, and the image cleaned up a little, but I still can't get the colors dialed in properly. There's also a pulsating blue horizontal line that shows up at the very top of the screen when the TV is first turned on, and it goes away after a while.

Also, I noticed that the screen control (which is on the neckboard and not the flyback) doesn't seem to have a large range. It either goes super bright with retrace, to bright, to completely blanking the picture.

Just for fun, I measured the cathodes and the red cathode was always at least 10-20v higher than green and blue. I'm not sure if this is normal as I'm still learning all this stuff.

TLDR: What are some ways to determine if the picture tube itself is on the way out, vs some other problem?