Congratulations!
I wouldn't say you have no chance of landing two F seats, but agree with others that it could be tough.
At this point, your best and least stressful bet for trying to find F might be an award booking service. Here's the thread here at FT in which some are recommended:
http://www.flyertalk.com/forum/trave...e-reviews.html
Regardless of whether you use such a service, don't confine yourselves to flying out of LAX. Depending on the airline, there's a chance you can find better options out of SFO, SEA, DFW, ORD, etc., (or returning to such places) if you don't mind taking the domestic hop to get to these places.
Finally, check on what the weather is likely to be like in Bali during our winter. I believe it's the rainy season there. Here's one of many sites that provide monthly temp and precipitation averages:
http://www.weatherbase.com/
Hope it all works out!