I have done some experimenting with the transformer-based oscillator and have had some success.
I used a small metal box RF inductor from a tape machine with one coil measuring about 4.5 ohms resistance.
Using that as the larger winding with the diode across it in the original PYE schematic, I wound a secondary coil over it.
I used #38 awg magnet wire and wound 27 turns and attached them to the unused terminals on the other side.
Keep in mind that the direction of the coil affects if it will oscillate or not, so some experimentation may be needed there.
Right now the frequency output is around 230KHz, which is right in the ballpark for proper function of the circuit.
The coils I used had a screw-adjustment cover over the coil, which can change the frequency a bit.
Hope this helps anyone looking to try the original oscillator design for this circuit.