Sounds like you're assuming a much lighter load for the inverter than the Listeroid. In your initial post what is 1500W? I'm confused as to whether you have a 1500W inverter or you're saying your genset it 1500W. On your web page you say it's 15000W. Did you lose a zero?
I'd suggest an inverter/charger like Xantrex's DR1500. I'm told Xantrex is discontinuing that line of inverters, but there are others out there like the DR series. It is modified sine but mine runs my water pump without a problem.
Since the DR is an inverter charger, use it to charge and use a much smaller pure sine inverter to run your TV, computer and anything else that needs the pure sine. You'd have to manually transfer loads to the pure sine, but the DR would switch automatically. Makes for a good UPS.
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A note to the guys who would power their houses with a pedaling wife, have you ever calculated how many watthours of power you get from pedaling? Just curious.