kW and KVA are interchangeable if you're driving purely resistive loads.
Reactive loads (capacitive or inductive) are a different matter - this is where kW and kVA separate and the power factor comes in. Some crappy motors have terrible power factors (0.3). Fluoro lights, computer power supplies,etc all have power factors that can make a generator (or inverter) sweat a fair bit.
For example, operating 400 Watts of CFL might require 600-800VA or more. Large motors might have a very poor power factor when starting, needing a lot of VA per watts at that time, etc... (Here the extreme importance of the surge capacity for an inverter when you operate large motors)
For your case, twiddling the windings around shouldn't affect the rated KVA/KW output (much....). Instead of two windings in parallel for 110V at a certain current to give you a rated power, you've two in series for twice the voltage , but only half the current.... but still the rated power.
Having said that, I've never had a look inside a ST head, so things might be different in their particular case.