HEY MR. needsacureforsomething-
What you really have is more of a circadian rythym problem than classic insomnia. You don't have a regular bed time and you don't have a regular 24 hour solar day when you bounce across time zones. Your hypothalamus probably has no idea what time it is anymore.
Lunesta may not be your drug. Ramelteon (Rozerem) is a pharmacologically novel prescription sleep aid hot from Japan. It is a melatoninergic agent. It makes OTC melatonin look like kool aid. It is more specifically suited to circadian disruptions than a sedative. It resets your "clock".
A lot of people from northern latitudes (and people with Seasonal Affective Disorder) use blue light phototherapy to maintain sleep patterns. It is also recommended for jet lag.
As far as general insomnia goes the usual drugs that the asshole doctors throw around are sedative hypnotics, which are usually just benzodiazepines or (very rarely) barbiturates (GABA-ergic drugs). There is a littany of other unrelated drugs that cause sedation as well: every antipsychotic, anxiolytic, beta blocking antihypertensive, anticonvulsant, narcotic, and antihistamine. Lunesta is just another sedative/hypnotic, just like Ambien.
Try the blue light- the worst it can do to you is cost you money. I was skeptical, but it helps me a lot when the seasons change and my bipolar disorder starts cycling. It will JOLT your brain awake in the morning. You just sit there for 10-15 minutes and let it shine on you indirectly as you check your email on your laptop and drink your coffee. I have never experienced anything like it before. It's just a light but it is a very narrow frequency of light. Animals seem to be weirdly attracted to the light as well. My cat loves it. Mine is a "go-lite" from Apollo Health. It's travel sized and comes with a case.
Siete Azaharres is a traditional Mexican herb tea blend that I have tried. It has a modest kick and its tasty. It has passionflower, valerian, linden, manzanilla (chamomile) and some other stuff in it. I can always find it at the yerberias and Mexican markets.
I've also tried supplemental GABA and 5-HTP and it really does nothing for me. Just gimme my damn dirty drugs!
Nietzsche recommends: "No small art is it to sleep: it is necessary for that purpose to be awake all day. Ten times a day must thou overcome thyself; that causeth wholesome weariness, and is poppy to the soul".