Our pediatrician gave us permission to give some more melatonin at 3 am. However, you might want to try gradually decreasing the evening melatonin. You can buy it in a liquid form and that way you can ramp down.
Some people give a little bit of Benadryl, but this revved my child up when we tried it at age 2.
If your child takes a nap, perhaps eliminating the nap would help. 9:30 strikes me as a late-ish bedtime for age 3, unless there's a consistent nap going on. If there's no nap, then perhaps what's going on is that the child is short on sleep. This can paradoxically cause sleep problems.
You can use stories and books on tape as a way of keeping a child calm without a lot of light and stimulation when insomnia hits. It should be a story that's so familiar it's gotten just a little boring.