I have a boxer, which has a similar digestive system (can you say GAS???). I've found that a moderate protein level helps, as well as a good brand of kibble. I was a long time Taste of the Wild fan, but recently, my senior boxer was having trouble holding his weight on TOTW Pacific Stream. I'm now transitioning him slowly over to Acana Chicken and Burbank Potato, and the change is already evident. He's pooing a LOT less already, even though I'm only at the 1/3 Acana 2/3 TOTW stage. Poos are still firm (another problem with boxers and other bully breeds). I have not noticed any gas, which is also a good thing. Fingers crossed that this improvement continues.
Another kibble that may work: Acana Singles kibble. There are three different varieties to choose from. I may rotate all of these.