I see my images (post #7) disappeared. I plan to re-post my screenshots later because right now they seem to get lost in transfer.
While On-resistance is important (should be very low), your high current draw could come low Off-resistance, that is, from the mosfet not turning off entirely. You say the gate drive is fine, however there may be stray capacitance which slows the mosfet's turning off.
Your schematic looks as though it will work.
When I have attached a full-wave bridge to the secondary, my simulations show the secondary has its greatest current flow while the primary is shut off. (And I have seen the same thing stated in an article.) This can mean that your diode direction makes a big difference.
While you are still in the experimenting stage, I suggest that you see how it affects performance if you attach a full-wave diode bridge. As to waveforms, current draw, net efficiency, coil heating, possible saturation (per post #2), etc.