With an RDS(on) round 6 mohm max, my conduction loss with will be somewhere in the running range of 5 to 30 watts depending on the power being requested (in this case 240 watts and 600 watts respectively).
Don't forget that the mosfet is not the only resistance in the circuit.
Conduction losses include everything the inverter input current has to flow through.
With the transformer high current primary, skin effect can be a problem in that the real working resistance of the winding can be much higher, sometimes several times higher than the dc resistance.
Another point to ponder, is that all these conduction losses rise at the rate of current squared.
The most efficient way to transfer power with minimum conduction loss apart from pure dc, is with a 50% 50% duty cycle square wave current. Where the peak current is no higher than the average. Peak, rms, and average are all the same.
Anything else, including sine waves, will have a higher rms than average.
Your inverter transferred power (real watts) will still be the average dc input current multiplied by the dc input voltage.
Conduction losses will be rms input current multiplied by voltage which is highly dependant on the current waveform.
Any current switching waveform that has a lower duty cycle, with higher peaks with a lower average will be more (conduction) lossy than a square wave for the same transmitted power.
Its the single reason why most very high power switching power supplies use forward converters with (almost) square wave currents, especially where the input is a low voltage at relatively high current.
Even with perfect sine waves the conduction loss will be 11% higher than with perfect square waves where the same power goes through the same transformer at the same voltage and frequency. Rms and average are not the same thing.