Hi LH, I don't know about the heat of the windings, I would think that the PVC insulation would definitely keep heat in, but then it will depend on how long the inverter is being run at high power levels.
Of course magnet wire would be much easier to work with but getting it in such heavy guages would require many wires in parallel.
When I wound large electric motors and generators the wire we used was often solid fibreglass covered rectangular section.
If you were to find a motor rewinding shop nearby that did large motors they may have some on the end of a roll that you could get.
Using just one wire is probably easier to do a neat job than lots of wires in parallel, but then you are only doing a few turns if Oz's core is anything to go by.
If you work out the current capacity you want, then you can substitute any wire guages that come up to that.
I used to look up a chart that gave the sizes of the wire, and also the area in "circular mms)
So if the wire size you want is a certain area, then whatever adds up to that size in circular mm's is the go.
Often if we did not have enough rolls of the right guage I would use different guages as long as they added up to the same area.
Pete