Internally, the video signal is the ol' composite video, nowadays referred to as AVI.
I know this is a stretch but bear with me
Have you looked at the signal on a scope to see if the apparent blank space on the left is actually real? Maybe the VNA compensates for this and what you see on the LCD is "true". Maybe it does this deliberately to provide more leeway for adjustment.
Do you have another CRT with composite in (like the 1997 Sony Trinitron that is my primary - and only - TV) or a flat screen TV with composite input to see what they display?
Another thought is that the composite signal is purely for external use and the internal CRT is driven by something else.
Internally, the video signal is the ol' composite video, nowadays referred to as AVI.Searching Google for "composite AVI" returns nothing relevant to analog video on the first page.
Searching for "CVBS composite" returns 20 hits that are all relevant.
I think you need to adjust your search terms.
I had the same problem as you when using a Commodore 64 with various LCD TVs.
I use an external video conversion device to connect to a computer monitor.
For example
https://www.ebay.ca/itm/Inline-IN1402-Video-Scaler/312791573324?hash=item48d3d4a34c:g:qtEAAOSwxlxdllEK
Manual
http://www.audiorama-berlin.de/pdf/1402man.pdf
Maybe you can connect your VNA to a box like that? Then you won't be relying on the LCD panel's interpretation of the video signal.
It arrived yesterday. Unfortunately the seller sent a different board, one which uses an SSD102 processor. I can find no info on this video processor. I wrote and asked him, he said it's an "updated version". Yeah, right.
I tried it out, and it does work better than the LCD display in the first post a couple years ago. The display quality is better. It positions the Horizontal display correctly. The vertical is positioning is wrong, still shifted up but a little bit less. Most of the top line is still missing, with blank space at the bottom.
So it appears that these video processors all do some sort of 'automatic' horizontal and vertical positioning, but not all do it the same.