Thinking about the lack of screen burn, maybe this tube has some life. I can't be sure what part of the system this screen was used for but worth having another look.
Putting the scope on the Cathode, the voltage between black and white screens is confusing me. Black screen appears to have a constant high voltage between the blanking periods,
Black screen

and the white has a signal that falls towards the 0V (E)
White screen
However, looking at the circuit, the video signals drive a push pull amp with the contrast setting the gain from a 5V signal. Interestingly, there is a 5V adjustment on the board.
Tweaked up the 5V and the screens contrast has increased
Looking at the signal at the cathode, the voltage has risen about 10V.
With all the messing about with the yoke, the linearity is a bit off and might be over driving things a bit, but hey it works.