what you could do is take draw reigns and instead of running them underneath his front legs and attaching to the girth, you can run them outside and attache them at the sides of the girth... that may help....You can do it with bungees too...
It is generally considered a no no to ride in side reins as the rider cannot "give" to the horse when necesssary. I have seen riding schools use them in this manner but more as a protection for the horse against a beginners unstable hand.
Farmpony............................. these are called auxillary or running reins.
Useful in the right hands but do require a knowledgeable rider/trainer when using them.