For an RH-84, I'd design it for 325VDC, at least 100 mA, wouldn't hurt to have more available current.
A 10VAC CT filament tranny (at least 5A rating, 10 would not be excessive) from Hammond should be a good choice here.
Since the plan is to run it at a higher "AC" frequency, the normal turns-per-volt formula for 60 Hz can be stretched by (roughly)
a factor of F(hz)/60, though the core size doesn't become any smaller.
I'd consider connecting a .001 uF 1KV ceramic disc cap across the HV AC output, in order to tame the possible "ringing"
and reduce the possibility of getting a whine or buzz worming its way through the rectifiers and DC filtering.
With this circuit, the AC wave form will be more square wave, than sinusoidal, peak-to-peak voltage
versus RMS voltage calculations aren't necessary. WYSIWYG
An open-frame tranny will probably howl or buzz with higher frequency
operation, I'd suggest to build the PSU on a separate chassis.
I have a couple of "real" inverter transformers, but they were designed for using germanium power transistors,
though they should work with this circuit, operating about 2 KHz. One is a potted Triad TY-78, the other one
is open frame, and can handle considerable power, about 150VA, at least. IIRC, this was good for 600VDC and 300VDC.
I long ago lost the data sheet for it, so some experimentation will be needed.
The HV inverter power supply that I built with the other identical transformer, I sold at a hamfest back in the 1980s...
The car radio was probably designed for use with 2 ohm speakers, and the "200 watts" must use the same kind of Roswell UFO
alien technology as my "400 watt" computer speakers, which are powered by a 12VDC, 1A brick
/edB