I'm skeptical about the 30uf capacitor suggestion. If the inverter is outputting a square wave the cap will likely draw a pretty large transient current, which could (eventually) damage the inverter. Here are some numbers to think about....
If the capacitor is driven by a 60Hz sine wave @ 120VRMS it will consume a peak current of 1.9 amps. Not too bad, right? But if the capacitor is driven by a square wave that changes 240V in 1 millisecond (pretty slow), it will take a peak current of about 7.2 amps to charge the capacitor from -120 to +120V or vice-versa. If the inverter waveform switches in .1 millisecond, the peak current will be 72 amps! It gets worse from there.
I think the idea is to produce a brute-force filter that tries to coerce the inverter waveform to more closely resemble a sine wave -- but it will likely be pretty hard on the inverter. I bet the warranty would not cover failure due to that kind of abuse.
Here is the math: current through a capacitor = C*dV/dT, where dV/dT is the change in voltage divided by the change in time. C is the capacitance in Farads. So if the inverter output switches from -120V to +120V in 1 millisecond, dV/dT = 240/.001, or 240,000 volts/second. Multiply by 3x10^-5 Farads and you get 7.2 amps of peak current.
I'd suggest trying the inverter w/o a capacitor and see how it works. If you MUST filter the inverter's output, use an LC (inductor-capacitor) low pass filter. The series inductance will isolate the inverter from the capacitor and the inverter will be much happier for it.
Or just use your generator and bypass all this.