I'd second the suggestion for trying pre-prepared raw, or suggest you try a very low-carb food, like Wysong Epigen, Evo, or a canned food. Yeast feeds on carbohydrates. These grain-free foods (e.g. Wellness Core, Natural Balance LID) are all very high in carbs-- they replace the grains with very starchy foods like peas and potatoes. Since the dog's system is loaded with carbs, that provides fodder for yeast to grow. Hence the itching and the ear infection.
I don't necessarily think the feeding trial with a novel protein source is a bad idea, but I'd hesitate to go down that road unless you're absolutely sure it's the *protein* Jack is responding to and not the other ingredients in the food.
Evo has some balanced 95% meat canned foods. Evanger's also has some balanced canned foods that are 90% meat or greater (e.g. several varieties of their Super Premium line). Evo kibble is low carb and Wyson Epigen is starch-free, and advertises itself as the lowest carb dog kibble on the market. Orijen's varieties are also relatively low carb. Most of the pre-prepared raw varieties will also be much lower in carbs than kibbles, and should you choose to be adventurous, going prey-model raw will eliminate all of the carbs from his diet entirely.
Here is a VERY simple raw dog food recipe that is supposed to starve out yeast:
Yeast Starvation Dog Food Recipe - Homemade Dog Food
It should be relatively inexpensive to try.
It might be worth looking into a high carb load as the source of your pup's yeast issues before going down the "food allergy" route. Very few dogs have true allergies to food, although they can develop intolerance to protein sources. I'd say if his stools are firm that would suggest more that he's having trouble with carbs feeding yeast as opposed to the protein in the food. If the protein source were giving him issues, you might suspect he'd have loose stools as well, because it would irritate the lining of his digestive tract.
Good luck, and keep up updated!