I have the same problem with mine. I wash her wrinkles above the nose daily with baby wipes (alcohol and scent free)
I also bath her once a week with NUVET shampoo.
I started feeding her nutro herring meal food and it has helped.. The food stinks sooooo bad.. but her coat and smell has greatly improved.
A bath with every week won’t hurt him if you use a good shampoo..

Do you think he is farting and smelling like that? Or is it his breath? Or coming from his skin. He could be allergic to something in the food. If he can’t digest something in the food, even the very best food won’t agree with him.
And the poor thing doesn’t need a weekly bath. That could also be part of the problem. His skin is dried out and is creating too many oils because it is being washed too often.
I would stop giving him so many baths. I would think other than cleaning his wrinkles, a bath every 2 or 3 months is plenty. If that doesn’t work, try feeding him a vegetarian dog food to clean out his system and then add one protein source at a time to figure out what he is allergic to. http://www.dogfoodproject.com/
Add Of course the shampoo maker will say it is OK to over wash the dog. That’s how they sell product.

That’s weird because we have a pitbullxmastiff and his feet smell like doritos ( corn chips) we have also wondered why!

I suggest you to use different kind of shampoo and conditioner.