So...hopefully you didn't dig into that circuit too much
It should have been obvious, but that circuit will also lose the DC level over time.
Cathode driven DC restoration is indeed a little bit more difficult since the set requries the cathode voltage to be about midway between the video amp plate and GND.
Anyhow, I gave it some more thought. We need a way to clamp the DC level to a reasonable voltage that is stiff. What I came up with uses the same 2 470k resistors to set the cathode bias, but rather than come off the video amp output, the 'top' 470k connects to C40 -- the same place the brightness pot taps off of. Those resistors give you a voltage at approximately half the video amp screen voltage, which is then stiffened by a 5uF (or so) 250V or better electrolytic.
D1 clamps the black level relative to the new 250V point. C2 and R6 set the time constant of the DC restoration (it's set similar to other sets of this era). The comments about R5 still stand - bigger R5 gives worse DC restoration, but might give better video and/or avoid synch problems. Give it s spin and see what works.
I've attached the new schematic.
I attached some simulated waveforms of what you might see at the original cathode and at the cathode with this circuit. The DC restoration isn't perfect, but it should be better than what you have.
I created some simulated composite video with positive synch (like you should have at the output of your video amp). The simulation has a bunch of lines of high brightness followed by a completely black section of video, where there is nothing above the synch pulses.
The original composite video is at top, the DC restored cathode signal in the middle, and the original circuit's cathode at bottom.
I'm not sure the AC coupled composite simulation is entirely accurate...but at least it shows how the set's original video amp causes black to fade to gray, while the new circuit eventually finds the right black level after an abrupt brightness change.
Nothing's perfect, hopefully this is something that others can common on and improve upon. After looking I was unable to find any actual schematics of cathode driven sets with DC restoration.