So here's something about melatonin that most people are not familiar with. They think it just doesn't work for them, but the reality is, they don't know the proper dosage. Melatonin can be very effective, and is not bad for your health, if taken properly.
First of all, just use straight melatonin, not the type with all the mystery stuff added. It is easier to figure out how much you need to take. Everyone is different, and you need to titrate yourself in order to figure out how much YOU need.
To titrate yourself, start by taking just 1 mg. Do this for 3 nights. It probably will have little effect on you, but some people can't even take 1 mg. It gives them crazy, wild, vivid dreams that are too disturbing. You don't want that. You want to take enough that when you wake up you feel fully rested, and have dreamt. If you wake up in the night, you go right back to sleep, instead of staying awake for an hour. That's the goal. After 3 nights, you take 2 mg for 3 nights, see how that feels. Keep upping the dose 3 nights at a time until you figure out your desired dosage. Some people need many mg to find their perfect dose. I only need 2 mg, at 3 mg, my dreams are too intense.
It takes about an hour to take effect, and you should have a good 8 hours available to sleep. If you have less than that, you might feel groggy when you wake up. I would figure this out when you have some time at home, not when you are flying nights, because there are too many variables when sleeping days. But when you figure it out, use that dosage to sleep during the day, and I suspect you will stay asleep a lot longer. I take melatonin every time I'm going to sleep, not just when working. As you age, you have less melatonin in your body. And sleep is critical, not just at work, but all of the time.