There is definitely a currency exchange at LAX as I had to turn my Fiji dollars back into US when I got back. LAX is major hub from west coast to Fiji so they must have currency. I can't remember if it was Travelex or some other. The ATMs give you the better exchange.

Be prepared for slllllllllloooooooooowwwwwww customs processing at Nadi, even at that hour.