To answer your question...Orijen. It's probably the highest protein food out there. There are 2 down side...at least for me.
1. IT'S EXPENSIVE!!! $85.00 for a 30# bag. But that's a small price to pay, since I love the results.
2. Because it's such a high protein food, it doesn't take much for them to be healthy. As a result, the dog will "seem" hungry, but definitely isn't starving. And with such a high protein food, if they aren't using it, they will get fat FAST! I've experimented with a few options to help Gunnar feel "satisfied" after eating. I have spoke to many trainers, as well as, a few vets. One solution I found that works pretty well (it's does have it bad effects too) is to allow the food to re-hydrate a little before allowing him to eat. This starts the swelling process and in turn causes him to feel full after eating. The down side is that dry kibble is also has teeth cleaning properties. To off set this, a chewy is given to him daily to help keep his teeth and gums healthy. After owning a few dogs, I have never brushed their teeth or gums, and they have never had bad "Dog Breath".
I have had troubles with food for my weim, Gunnar. Started on Innova, moved to ProPlan Performance, then tried Taste of the Wild (grain-free), and finally ended on Orijen. By far Orijen has had the best outcome for Gunnar.
Orijen Dog Food | Review and Rating
As for you other concern...the gas, check with a vet. Could be allergies, or just a sensitive stomach. My Doberman had a very sensitive stomach, and after 20+ foods...Eukanuba Performace was the only one he didn't have a problem with.
This is just my personal experience, check with your vet if you need real answers about your dog and their situation.