3-phase Inverter in single phase operation
It's absolutely common to derate three-phase inverters for single-phase source operation. The front end (diode bridge) is under more stress because all the current now only comes from 2/3 of the diodes. The DC bus capacitor also takes more of a beating due to higher ripple current since you're missing a phase that helps keep the bus charged. When I worked in this industry we usually derated the drive 33%, possibly more if it was for a constant torque application.

There are usually line reactors or a DC choke as well, as you've mentioned, but I don't think I've ever heard of rewiring or trying to use the now-unused third phase coil for anything. Even if you were to try to put it in series with one of the other phases you would introduce imbalances in how the inverter is taking power from the line.

I guess the bigger question is what you're trying to achieve by using this unused third coil? I don't think anything useful can come from it, and in fact if you're going to go to all the trouble to rewind it for marginal gain you might just be better off using a DC link choke instead of the line reactor.