
I don't quite see the logic in reducing the protein? My dogs are fed Orijen along with raw tripe/fish/meat and don't have this problem if I use cooked meat for training. It is more likely they are getting too much food full stop, if they are having their usual daily allowance of Orijen, followed by an additional amount of "training" food. By swapping foods I can't see how this would help.
I would suggest on training days reduce the amount of Orijen fed and see if that helps.