Hi,
The SG chip has built in regulation circuitry. All you have to do is provide some feedback possibly filtered. If the feedback constant is right it will regulate at around 120vac (assuming that's what you want) and you will obtain your modified sine because that SG chip will automatically cut back the pattern to a shorter pulse to get the right voltage output.
To start with, you'd want to full wave rectify the output so you can get a Dc feedback voltage. It will be pulsing so you have to do a little filtering too.
Once you proved the SG chip with feedback it will cut back as required, the theoretical duty cycle is 83 percent but it may vary a little with load.
The typical patterns are about 80 percent duty cycle for each half cycle, and about 145v pulse height. That's typical on the modern modified sine inverters.
Of course you have to provide phase switching to switch the output from a positive pulse to a negative pulse, but that's just keeping track of every other SG pulse and steering it to turn on the right set of transistors.