A solution to that is to make it more like they used to do AM
broadcast transmitters: feed the RF stage its DC through an audio
choke, and capacitor-couple the audio into the RF deck end of the
choke (from one of the plate connections on the audio transformer).
If the audio amplifier and the RF deck use the same plate voltage, the
capacitor doesn't need to handle the full DC voltage, but it should be
non-polar. The problem then becomes one of finding (or winding) an
audio choke with enough inductance and that can handle the current.
In AM broadcast transmitters, the modulation choke was typically the
largest component. Since for voice you should only need to get down
to 300Hz or so, 10 henries inductance should be OK (about 20k ohms
impedance), and you might be OK with less. A 4.7uF coupling capacitor
should work OK, as it would be just over 100 ohms reactance at 300Hz.
4.7uF film capacitors aren't unreasonable to find. You wouldn't ever
get to 100% modulation, since the audio side doesn't go to zero volts
on the plate of the conducting side, but you could add the voice coil
winding in the proper phase to get a bit more modulating voltage.
I've also seen a design where the modulator was single-ended but used
a push-pull transformer; the RF amp was fed its DC through the other
side of the center tapped winding. That allowed reasonable balance of
the DC in the transformer, and worked decently.
Cheers,
Tom