We extended on the way back (helped with culture shock too, as Bali to the US is a huge difference). When you book on the Sing Air website (the best way, as you can choose your seats too), use the custom itinerary and build the flight in its segments. I think it's easier to do on the way back as the flight cost is based on your outbound destination, but I'm sure one of their booking agents would help you if you want to do it on the way there. You'd have three segments: LA to Bali (which changes planes in Singapore), Bali to Singapore, Singapore to LA. There was no price change when I did it that way.
it's very strange - the stopover for the inbound flight is $700 less than the stopover for the outbound flight
Maybe based on one of the segments? Did you try various Bali/Sing combos -- different departure times? Maybe one of the flights is very full so there's a premium on it?
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