Agreed, a flyback is way off the mark, what you are seeking to do is a fairly major power electronics design undertaking....considered hiring a power electronics engineer?
A transformer is surely required. The point was about using push-pull instead of flyback. And of course, 30 kHz 4kW transformer design isn't easy going.
How are you planning to switch 125 amps? at 30kHz, for a conventional H bridge the voltage drop due to XLxI will be quite high... as will be turn off volt spikes due to high current and wiring inductance...
I think, H-bridge is the obvious solution. And for a fixed converter voltage ratio putting transformer leakag inductance into a series resonant circuit with capacitor on the secondary side.
The capacitor will charge quickly at turn-off. Then it will discharge through the resistor.
Select cap value so it rises to supply V (give or take 50 percent).
Select resistor so it bleeds charge down below 50 percent of supply V.
If capacitor is small, and resistance is high, then the charge will accumulate after many cycles, to a hazardous level.
If resistance is low, then undesired current will flow in the primary for a while after turn-off.
The diode must be rated to carry the maximum expected primary current at turn-off.
Considering your output power is 150W, then the resistor must be rated for several watts.
Zeners back-to-back are useful when testing. Their purpose would be to prevent the capacitor from charging to too high a level. The zener voltage should be greater than supply V.