SWEET! I can walk from my house!
Despite what Google Maps claims, lately the best route from DMS to the park has been Josey, Belt Line, Kelley. Even through a school zone that route has been consistently faster / less aggravating than 35, Bush.
Going Josey to Keller Springs crosses the railroad tracks twice which raises the possibility of waiting for a long slow train. Don't go that route.
Even on weekends there is ample parking at the school. The parking lot at the park is usually full.