An inverter is possible. The schematics I've googled are push-pull with a center tapped 24 volt primary. It would have to be pretty heavy current, probably 20 amps or more. It would probably be easier and cheaper to run the mobile amplifiers filament string from 12 volts directly, and use a commercial inverter capable of decent clean sine wave, into a normal high voltage transformer.
I just looked up the 6384 ... sounds like it's a a heavy duty 6L6GC (different pinout) ... there are quite a few on eBay, prices all over the place. Is that what you'd use in the car?
I thought about a car amp a few times, but the space and current requirements make in impractical for me.