I'm running a 6-1 ST5 charging a 48v battery bank through a pair of vfx3648 inverters. My engine will run clean, once warmed up, putting out a steady 3120 watts. I've run up to 3400 watts, with a bit of black smoke. So it seems the 3KW head is a bit undersized. Also the stored energy in the flywheels will allow surges to quite a bit higher than 3KW. So I'd suggest you go with a 5KW head.
On my inverters I was disappointed to to discover that a feature I consider essential, generator support, is not currently enabled. What that does is combine the inverter and generator outputs to support larger loads than either could alone. Since I'm using 2 inverters I only have 13 amps per leg when on generator power. When I turn on the microwave it will draw the voltage low enough that the inverter/charger will trip out on the low voltage setting (108V) and go into inverter mode until the generator speeds back up. It then starts the cycle over again. If I had a 3KW gen head this problem would probably be much worse.
If you haven't purchased outback inverter yet, the xantrex sw series inverters do have generator support built in.