There are apparently IGBTs suitable for (if not necessarily _specified_ for) linear operation. But MOSFETs or BJTs are better here.
BJTs are better at somewhat lower voltages, but I think you can find some with an SOA up there still.
MOSFETs and BJTs have no palpable difference in efficiency. You're making, at best, a class B amplifier; your peak efficiency will be around 60% (I forget the exact calculation, is it up to 66%?). Getting up to 50% is practical.
You are building an audio amplifier, whatever you may think of it -- a linear sinewave amplifier is just like any other amplifier. The fact that you're using it at a fraction of its bandwidth, doesn't really help in any practical way. (Even if you have more of those 1H high current chokes, and they're high enough Q to make essentially an RF amplifier but at line frequency.)
What the heck is the massive choke and cap for? That sounds like more of a liability than anything to me. If I were designing an inverter to run from such a supply I would at the very least add a very meaty TVS to the supply, in case that inductor lets its energy out unconstrained (say under fault conditions). Likewise for the capacitor, a fuse at least but preferably some means of limiting fault current as well, if for no other reason than to minimize damage when something dies.
Just how much power are you looking to get out of this thing?
Tim