I couldn't find a schematic for the LBO-402, so I'll use the one that's available on the web for the LBO-401, which, I presume, must be similar, regarding HV.
Below we have a block diagram of the HV circuit.
Q406 generates a constant current that flows through R in the block diagram, which corresponds to R420 + VR404 + R419 in the schematic. This creates a constant voltage across R. The voltage on the base of Q403 (point A in the block diagram) will be around 2V.
If the voltage at the HV output gets more positive than -1500V, point A will tend to be more positive which will make the oscillator increase its amplitude, making the HV more negative until it returns to -1500V. If it gets more negative than -1500V, point A will tend to be more negative, decreasing the amplitude of the oscillator.
What would cause the HV be more positive than -1500V? Anything with a path to ground or to a more positive voltage. C408 and C417 should be seen as suspects. It seems that C417 has already been replaced. Q405 should also be inspected, as well as the CRT itself. There could be a short circuit between the filament or the cathode and other more positive element, like the astig or focus anodes.
Finally, the transformer and its potted voltage doubler. C406 could be the culprit but also D401 and D402, if they are leaky.
What I would do? I would remove the CRT, Q405 and the jumper between R417 and D406. This will isolate the HV circuit from its loads. Then, before turning on the oscilloscope, I would turn VR401 so that the voltage at the base of Q406 would be +27V when the scope is powered. This will make the HV be at its minimum, perhaps even at zero volts, since Q402 and Q403 would be cut off.
I would then turn VR401 gradually until, say, 325V at the TP 402. That would give exactly 100µA through R. Then I'll measure the voltage across R417. It should be 39V. It it is more than that, especially much more than that, C408 is leaky and should be replaced.
If C408 is OK, I'd be turning VR401 until the voltage across R430 (attached to the emitter of Q406) reaches 15V (noticed how R430 is approx. R = 3256000 ohms divided by 100?). That should give you around 1500V at TP-402. If it doesn't, then to check the forward path between the base of Q403 (point A) and TP-402. If Q401-Q403 and the components around them are OK, its time to seriously consider to check the voltage doubler.
Since R427 is not potted, it is easy to check if one of the capacitors are leaking. Nothing must pass between ground and the point of contact between the resistor and the transformer. If the capacitors are OK, it is possible to check the diodes by applying some negative voltage between the thick red wire and ground and measuring the current. This test however measures the two diodes in series and can only detect if both are cactus. If one is OK and the other is shot, then only surgery on that potted doubler would tell.