Hrm... I think you've missed my idea. Even though the structure is laying horizontally, like an aircraft on a runway, no horizontal motion takes place during launch. It just lifts off vertically and then rotates 90 degrees to decrease drag.
You'd need a hell of a lot of JTO rockets to pull that off, and the risks would not outweigh the benefits.
I think that simply dropping the rocket out of a carrier aircraft makes a lot more sense to accomplish that, especially since the air-dropped launch allows you to always launch your rocket from the equator and potentially at a relatively high altitude which can increase your mass fraction by reducing drag and saving some fuel.