I think the primary should be similar to a normal 300W transformer because they are all the same on the primary, unless the secondary won't fit in a given geometry.
The secondary is probably going to be wound with way too many layers, some people that do ELF radio figure out the inductance of alot of turns, its ugly
Otherwise you find the maximum turn overlap you are comfortable with and figure out how long its gonna be for 30kV. I think if you just keep stacking layers up to make it whatever convenient size it starts getting weird impedance properties
I think reasonable would be 15-20 layers of windings. Then you figure out how big it might be.
Lets say you settle for 15 layers of windings, and a wire gauge, and a similar primary to a regular transformer. all you neeed to do is figure out how big it gets from there. I think you might be able to get somewhat close to a estimate.
A kind of math optimization problem that if you solve will at least give you theoretical first order extrapolated specifications. Then you can use a transformer calculator to get extrapolated theoretical impedance.
Your turns ratio is 136. Lets say 300 turns on the primary as a guess. Then you need 40,000 turns on the secondary.
If its 20 turns deep, then you need 2000 turns down. A clueless guess is 36AWG. That is 0.005 inches diameter. Meaning, 2000*0.005 = 10 inches . That seems kinda big. I guess they do it deeper and it gets worse. At 40 turns you get a reasonable 5 inch coil with a added diameter of 0.2 inches all around the secondary.
I don't know if any of this holds for high frequency transformer. maybe its nicer and more compact. But I think that should at least theoretically give you a 60Hz 30kV transformer
I think the # of turns on the primary for a high frequency transformer goes down. At 25Khz what could it be, like 50 turns? Then you need a measly 7000 turn secondary. But I don't think you can stack the layers so much at higher frequency? I will totally guess and say... 10 layers. Then its a 3.5 inch long secondary .
I wonder how I did