From the measurements I have taken I have determined the core used on the buggy steam resonator is an E65 Ferrite core, not sure which type of ferrite yet. The primary wire is 18AWG, while the secondary coils are 22AWG.
The high watt resistors suggest that there is not a whole lot of power used in this circuit, maybe 5 or 10W. I'm not sure of the watt rating of those resistors but if they are 5W then the max current at 80V would be about 62mA. If they are 10W resistors then we are looking at 125mA.
Looking at the PNP and NPN transistor configuration I can't help but wonder why Meyer didn't just use a push pull driver on the primary coil to achieve the polarity switching?