I don't know how you're probing those nodes, but I suspect the ringing you see is measuring error. It is tricky to get good CMRR in those kind of measurements. Try looking at one of the low voltage secondary windings on the output transformer, like the 8.6 V one. When things are right, it should be a very nice trapezoidal squarish wave with rounded corners. First find that good wave, and if it's not, then there's trouble, and you may be able to diagnose it from there - as long as you can have it running somehow, which seems to be the case.
The way it's supposed to work is that the base drive transformer saturates in each half-cycle to determine the oscillation frequency. It's basically a Royer type converter, but not using the big output transformer as the saturable device, which would waste lots of power, and make the waves ugly, It's really pretty slick, needing only the little transformer's saturation to make it work, and it also shorts out the primary of the big transformer at the right times to help clean it up even more.
The transistors are supposed to never saturate, but be close, or drop up to a few volts, depending on which of two different control schemes are used. One is where the switching transistors' drive is adjusted to drop the overhead to provide regulation. They have to then dissipate all that "series" power, so they do both linear regulation and switching. The other scheme uses a separate linear pass element to control the overall supply to the chopper stage, and it has to dissipate the excess power instead, while the switch transistors want to be just near saturation, to minimize their dissipation. I believe the switch transistors in all models needed to be selected or matched somewhat, to keep things from getting too lopsided, which could cause failure.
The chopper was to operate more or less the same either way, but can't exactly, with the different conditions. The outcome at the secondary should be about the same either way, nice clean waves with slow edges and rounded corners to minimize HF noise.
Ed