Hi Turnip.
The CCFL's could be the cause, one of the transformers or even the small pF coupling caps...... not saying it is. Never had a transformer go on me yet but sure have had coupling caps doing that.
Have you no spare tubes you can hook across to check? That is what I usually do, I know it's a pain but it does prove a point....
pity you couldn't load the inverter with resistors instead of tubes - dunno what kind of current they draw, you'll need high voltage resistors and resistance high values, but you'll need one for each tube, might even have a play, sure would save a lot of time and guessing.
Take note how the tube lights, if they light fairly even, do they flicker will point towards the tubes or inverter. Since you've had capacitor troubles, hows the voltages, especially the inverter supply? They are usually within a midgets whisker either way - so to speak.
In my case, I tried a new eprom to no avail my guess is the data lines being clogged up, so I'm gonna have to try another main board.
Edit:
I seem to think these sets comes under Baur brand as well as Baird.
Dave