Can a Cockcroft–Walton generator exhibit resonant rise?
That's a rather unusual Cockroft-Walton design.  All the ones I have seen are a single ladder with capacitors on the outside and diodes in the middle.  This design with the triple capacitor strings maybe has more current capability.  I'll have to think about this some more.

In any case, it looks like maybe this should multiply by 4.  I've got things to do, and that's just after a quick look, not a careful analisys of this unusual design.  The input is 33 V, presumably RMS.  That makes it 47 V peak, and 93 V peak to peak it it's a sine.  That times 4 is 373 V.  You are getting about 84% of that.  That sounds a little low for no load, so I'm guessing what is coming out of the transformer isn't really a sine wave so that the peak to peak voltage is lower than twice the square root of 2 times the RMS voltage.

In any case, it all looks like it's working at first glance.  I don't see how resonance has anything to do with this since you are outright measuring the AC going into the CW generator.  If you know what it is, it doesn't matter how it got there.  You should look at it on a scope though to see what the actual p-p voltage is, since this is what a CW generator works on.