The cure for overjumping is lots of calm, quiet schooling with a lot of gymnastics and/or placement rails to help the horse find the correct take off spot.
Horses are quick or fast in the approach of on course for one of three reaons, IME: 1.) First, they're frightened. If they don't understand what you're asking of them, or they're overfaced, their fright and flight instinct kicks in and they tend to get quicker and quicker. 2.) they misinterpret their rider's body language and aids and assume that the rider WANTS them to go faster. If the rider is unbalanced and leans on the neck or lands in the heap after the fence, it tends to make it worse 3.) the horse itself is unbalanced, lands from a fence in a heap on its forehand, and then speeds up trying to recover its balance, and with each subsequent fence, the problem escalates.
The solutions? Go slower with the training progression, make absolutely sure your position, aids and balance are correct, use gymnastics extensively, and focus on good quality flatwork and fitness, especially working on adjustablity at the canter. English style, forward, working canter, not a WP lope.
It can also be a combo of the three.
I would also like to second the poster above who questions whether this is a realistic goal or training program for a reining horse. You may want to settle for a reining horse that can jump a single fence or a log on the trail safely, rather than attempting to have a reining horse that can jump a course of fences.