Thank you everyone for all of your help. I hate to admit this, but I did not end up bringing kava on my trip. I chickened out. It seemed like too much trouble.
I decided to drink wine and then a bit later, take an all-natural sleep supplement (Dr. Price's Sleep Vites).
The first long flight (17.5 hrs), I ate dinner & had some wine, changed into sleeping clothes, took the supplement, and was feeling good and sleepy, but unfortunately, a rude passenger decided to laugh out loud to the movie she was watching for two hours, which kept jarring me awake just as I was falling asleep. After desperately trying to sleep for those couple of hours, the moment passed and I was not able to sleep again. The second long flight (13.5 hrs), coming home, was during the day, so it was pretty challenging to get any rest, even after a busy week of jet lag and sightseeing. I forgot to take the sleep vites and again relied on wine with lunch. No sleep. So I returned home with jet lag from a 14.5-hr time difference, plus the loss of two nights' sleep. I would do it all again for the chance to go there since it was wonderful, but next time I hope I'll have the kava thing down pat and can rely on that to get the rest I need.