This topology will not work for several reasons:
- It has no back EMF diode clamp
- The driver impedance is not low in the off state and even with diodes is not sufficiently low compared to this FET to regulate voltage with a load transformed (divided by) \$R_{load}/N^2\$. The ratio of source to load impedance determines the "% voltage load regulation error" This is critical to your understanding of boost converters and means the source impedance must be very low (in both hi and lo voltage states).
- The primary current should be symmetrical to improve power quality , reduce EMI and load resonance, eliminate DC, and preferably sine wave or 3 level switches.
Complexity of AC inverters is far greater than this and you might study how it is done before trying to DIY. A DC powered centre tap and dual Nch end coil low-side switches with BEMF clamping is a better topology. https://www.edaboard.com/attachments/12v-220v-gif.62924/