Those are not leaf miners, they are something else. If you can see the actual worm underneath the spot and can remove it by hand, then do so and destroy. Otherwise, I would spray, preferably with Spinosad. I'm thinking this isn't a really bad infestation, and you should be able to get rid of these pests. I do understand about the sentimental value of the plants. I have the flat rocks my fur babies were planted under in my garden.