Mist or water from the bottom as the seedlings grow. Diluted applications of fertilizer will encourage growth. But make sure the soil mix does not become overly wet. Transplant to the garden when they are large enough and the weather is mild. Since you've been having difficulty with seed, you might try starting with a couple of bedding plants.
Some perennial herbs can be especially slow growers when started from seed.
Rosemary is an evergreen perennial, available in upright or more trailing forms, that loves sun but accepts afternoon bright shade. A slightly alkaline, well-draining soil is best. While rosemary sulks when allowed to wilt, good drainage is the key to best results. You can increase alkalinity by occasionally adding crushed egg shells to the soil. It is winter-hardy in many areas of Texas, but if your plants dislike winter in your yard, try rosemary against a protective south or west wall, or grow it in a large container so you can more easily protect during especially harsh periods.