I hate leafminers! Only had them once many years ago and it was on edibles so traditional systemics were out of the question (Imidacloprid is evil stuff). Only one thing I found that worked, but it took a couple weeks: Neem oil
Mixed 2 Tbsp to a gallon of water with 1 Tbsp/gal of a safe soap (Like Dr. Bronner's, what I usually use), spraying it just before nightfall every 3-4 days.
Neem is perfectly safe and is mildly systemic (i.e. absorbs into the plant for further redistribution). Works in a strange way: It makes most insects forget to eat after 24-48 hours. Go figure. It also messes up their reproductive cycle by making them "forget" to breed. Amazingly, it doesn't affect beneficial insects.
Other than that, I have no idea what to do about those insidious bloodsuckers called leafminers. I'm not even sure there are any purchasable beneficial insects that attack them.
Good luck!