I know nothing of the subject matter - but reading this thread (a) cos it's a Sunday morning and too early to be making noise outside and (b) always interested in turret/toolchanger design for a lathe.

Given your last point, on the dirty output from an inverter. There's an easy and relatively cheap solution for that - depending on the power that you're looking for - pick up a 2nd-hand site transformer to take 220 to 110, then spec out a 110v in/out inverter. Yes, this comes at a cost for the transformer (relatively low) and the space required to house it - your call on that - but it resolves the problem.

There are VFDs rated at 220V in, 110V/3 out - at least so they claim, but I do take your point on dirty spikes. A decent set of filters could address that to some extent - but it's again your call on whether you trust that solution.

Another wacky idea that amalgamates both the above to give the worst of all worlds - use a 220V inverter and a three-phase transformer to bring it down to 110VAC/3.

Or replace the 3phase motor - though I'm guessing from this thread though you're trying a light touch on the turret assy.

Sorry - just random thoughts - none of which are particularly elegant.