Have you checked the plate swing over the full load range (intensity) of the CRT circuit? Since there's quite a bit of power dissipation in the HV windings, the output loading may not have much effect, comparatively, but it would be good to know what happens.
Also, you may want to consider and experiment with the value of the primary tank capacitor. Since the HV winding capacitance now seems to dominate the resonance, maybe less on the primary would help. Right now there are two (or three) tanks that are coupled to an unknown extent, each with its own resonant frequency. If you have equipment to measure inductance at low frequency (far below resonance), you can check the individual winding and leakage inductances, which would help to understand what's going on.
You can experiment by driving the plate (with power off of course) at low voltage with a function generator and some series R, while measuring various points with a scope, to see if there are any strange or multiple resonances, and the effect of the primary cap value. There shouldn't be enough power available to light anything up, so it should remain linear.
Ed
