Well, you're looking at about 1300 miles from El Paso to St. Louis, which is two very long days on the road anyway you look at it. Trying to get there "early" on the second day is going to be a problem any way you look at it.

I still would say stopping in Lawton would be better than trying to push all the way to OKC. Lawton will be about 13 hours on the road, and you'll be looking at another 11 hours or so to St. Louis, so you'll have to plan to leave early both days if you want to do this, have time to get some rest, and make it to St. Louis in early evening. Just know any way you slice it, whatever your evening plans are for St. Louis, you're going to have spent a whole lot of energy in your job trying to get there in this timeframe.