So a somewhat belated report.....
Well, it was another night with mixed feelings....
First we tried the chassis that still had the working fly-back. First we had some problems with the HV connection to the tube audibly leaking (sparkly sound). We cleaned the area around the hole in the tube (yes, was pretty dusty...) and that solved it mostly.
However the picture on screen showed still a vertical collapse. We only had a horizontal line and occasionally a couple of lines jumping up and down of that line. At least everything else seems to work

Vertical collapse is reported to be a pretty common problem on the K4900 (The 25K5515 is basically a K4900 adapted for med-res). So...gonna have to do some more research on that one.
Next Bart soldered in a fresh fly-back on the 2nd chassis. Installed it and.......YES we have a working picture and no fire-works on the fly-back

I checked the HV voltage with my trusty vintage Zenith HV meter (also very handy for discharging the tube between sessions) and it was exactly 25kV.
However, the picture was somewhat dim. The canopy over the monitor made that we could make out the picture, but it was sure not as bright as you normally expect.
Turning up the Screen pot on the fly-back made the screen white tinted and show retrace lines (was nice to be able to explain some stuff to Bart

). So....there had to be another issue...
Well, checked the manual (gotta love the iPad) and there are no brightness or contrast controls. However, there is a pot called "Black level".
Turning it showed absolutely zero effect. We took out the chassis and measured the pot while turning it and got the same value at every setting. We verified it on the other chassis and there we did see the resistance values vary as expected when adjusting the pot...
We were somewhat tempted to solder the good pot over, but cold, hunger and time had got the better part of us and so we decided to call it a day.
The next step is replacing all the pots. With hindsight, I had already said that I didn't trust them anymore from the first tests and I should have replaced them right away....
O well, never too late. Investigating what values I need and then ordering them for both chassis.
Tomorrow we will pick up 1 cab anyway, this will also help so I can test the chassis at home...
I have arranged a stylish US kind transport for tomorrow

To be continued...