A typical but improved approach would be like so:
I made this some years ago, which works fine. Build:
https://www.seventransistorlabs.com/Images/InverterProto1.jpg No driver was found necessary for TL598 into IRFZ34N. I did note the shunt resistor's inductance (a 10mΩ metal-strip type) was high enough to seriously affect turn-off performance, which needed a bypass cap there. Prefer chip resistors.
There's a UC3843 flyback for secondary side power, to run the oscillator and driver of a "modified sine wave" mains output. H-bridge output, US 120VAC target, hence the 170V supply here. Obviously that's not needed for a tube amp, and the direct DC output will suffice.
Scaling up output voltage is simply a matter of more secondary turns, finer wire, more inductance, and less capacitance. This doesn't come for free, as the winding length inside the transformer matters.
Winding length can be partly compensated by simply using multiple DC outputs in series. This may be desirable anyway, say if you need 300V for screen power. This reduces the maximum secondary winding length by N, and has the downside of using N rectifiers in series, and more inductors and capacitors (but the same total amount for given capacity).
I would encourage a flyback (possibly QR type) for higher voltages. Forward converters aren't great at high impedances: the transformer secondary needs quite high impedance, a contradiction for good transformer performance (low leakage is desirable); and the filter choke must be low capacitance as well (bank wound, preferably). For example, here's a ~20mH <80pF inductor I made even longer ago:
https://www.seventransistorlabs.com/tmoranwms/Elec_Compound10.jpgnot so easy to do with commodity parts (e.g. divided bobbins on standard shape cores).
You might also simply avoid the high voltages and select a lower voltage type for the amplifier, if this is an acceptable route. Sweep tubes for example have long been used in the SW band, perhaps with some neutralization as they aren't quite as RF-friendly as the proper types are; they're usable as low as 200V, albeit at some loss in efficiency.
Tim