Two possible ways:
1. You use a stand alone transformer and a stand alone choke with a diode between the two, the primary of the transformer runs at 5Khz and the choke becomes a low pass filter that runs at 10Khz then 20Khz self resonance. We know how to do this and we can build it.
2. On the 5 coil VIC you have got to isolate the chokes from the primary otherwise the load impedance of the chokes will be reflected back at the primary during pulse on. What if - the primary running at 5khz is not priming the core flux at all but is priming the secondary via proximity. You could shield the primary bobbin with a material that doesn't allow a magnetic field to pass then wind the primary right next to the secondary so its magnetic field works as an air core. A really narrow shielded primary right next to the secondary would suffice to get enough current into the secondary. Then the actual real core would act at 10-20khz using the chokes as low pass filters in the exact same way the stand alone transformer and choke does.
In Stan's 5 coil VIC is there not a narrow coil right next to the secondary that is as tall as the secondary and in close proximity?
I'll bet anyone that coil is the primary and it's shielded from the core and there is proximity magnetic field transfer going on.
It is the only possible way you can decouple the primary from the chokes on that particular VIC and Stan has done it to avoid two seperate VIC componants and for space saving.

I'll bet anyone they can get their 5 coil VIC working if they place a nickel shield between the primary and the core and place that primary right next to the secondary, make it really narrow but the same depth as the secondary so the windings are level where they finish. Then find what frequency the chokes are resonant at and drive the primary at one quarter of that frequency. Work out the LC circuit componant of the series circuit at 4 times the drive frequency and not double the drive frequency.

Look at the hole, it's nickel inside. What he's done is charged the secondary via proximity and shielded the primary from the core then he's used the core so the chokes act as an low pass filter for secondary current. He must be using nickel shielding on the choke side of the VIC too so that he can control how much inductance the core can absorb from the chokes at resonance. This is usually done in stand alone low pass filters with air gaps but because Stan has placed the chokes on the same core as the secondary he has to be able to isolate the reactance of the chokes from the secondary.
He's took the long way around with a 5 coil VIC, its easier with stand alone chokes.

Sorry, low pass filters not high pass.