I think an induction melting inverter wants first, variable
frequency (the metal load affects resonant-point) and
then -maybe- some power control, but that could be
crude on/off. Some smarts about finding the resonant
point, might borrow from MPPT schemes. Or hand on
the knob and eye on the dip meter....
Lots of videos and hobbyist brag pages on induction
melting, some show the electronics used. Go dig. If
you were really industrious you might chase industrial
induction furnace marketing and repair info, you might
find your way to a replacement controller / RF drive
board P/N schematic and BOM for something "above
hobby grade".