I know most gardeners consider Creeping Charlie [Glechoma hederacea] an annoying pest.
However, it has a very shallow root system, and could make a very good "living mulch". Keeps the sun from evaporating moisture from the soil, keeps direct sunlight from killing valuable microbes, keeps the soil cool so worms can feel comfortable, and chokes out other 'deep rooted' weeds. I'm putting in Chocolate Sprinkles Cherry Tomatoes.
Once your starts get higher than the max height of creeping charlie, would it be a bad idea to just let the two cohabitate?