Jaspers mom,
I can't tell you specific brands that are best in your price range if I don't know your price range. And also I don't know what they sell at your grocery store, but I hope you are not discounting getting your food from a petstore, because they are not neccessarily more expensive... You mentioned that you previously fed Purina One, so I looked up the price of it. It is actually fairly expensive for a grocery store brand, which means it wouldn't be a big price jump for you to switch to a premium brand. To give you an idea, I did a little math comparing Purina One (which you have already fed) to Canidae (which I chose because I happen to feed it, but it is just one of many great brands). I am also including alpo for comparison because it is the chepeast brand I could find all the info about online.
Since you didn't say how much Jasper weighs, I looked up the average for his breed is 50-70 pounds, so I am basing serving sizes on that. And for this example I am assuming you will feed the middle range of the suggested serving.
Purina One - $32 for 38lbs
They state 1931 kcal/lb, 449 kcal/cup. From that you can figure out that there are roughly 4.3 cups per lb
From that you can figure out 163 cups per bag.
The recommended serving size is 2 1/2 - 3 1/3 cups per day, which means an average of 56 servings per bag.
56 daily servings for $32 means 57 cents a day
The top 5 ingredients: Lamb, brewers rice, corn gluten meal, whole grain corn, oat meal
Canidae -$33 for 40lbs
The state kcal/lb=1875, kcal/cup 468, so you can figure out there are 4 cups per lb.
From that you can figure out there are 160 cups per bag.
The recommended serving it 2-3 cups, which means 64 servings per bag.
64 daily servings for $33 means 51 cents a day
The top 5 ingredients: Chicken Meal, Turkey Meal, Brown Rice, White Rice, Lamb Meal
Alpo Natural Flavor From Beef & Chicken Dog Food - $20 for a 40lb bag
They state that a cup contains approximately 95 grams of Alpo. That is 0.21 lb/cup. From that you can figure out that there are 4.76 cups per lb.
From that you can figure out there are 190 cups per bag.
The recommended serving is 3 1/2 - 4 3/4 cups, which means 46 servings per bag.
46 daily servings for $20 means 43 cents a day
The top 5 ingredients: Ground yellow corn, beef and bone meal, soybean meal, beef tallow preserved with BHA, animal digest
So from that you can see that Canidae actually works out to be cheaper than purina. And instead of getting a food where 4/5 of the top 5 ingredients are carbs, you get a natural, top-rated food with only 2/5 of the top 5 are carbs... And if you compare it with alpo, it only costs an extra 8 cents a day, which is nothing, especially when you consider how terrible the top ingredients in the alpo are! There are so many benefits health wise of premium brands, and they really don't cost more when you factor in the serving size because there is so much less junk in them!
With all of the health problems that you mentioned, I think it is really important Jasper gets a healthy food. I know that it is frustrating that he doesn't seem to like them any better taste-wise, but what's really important is how they affect his body, and a better food can only help his health!
I understand your frustration with getting bored of foods quickly. Many pets do, and you can't really blame them - I know I couldn't eat the same thing every single day. Zoey will often get bored of a food after a few bags of it. We solve the problem by supplementing with a few bits of dog-friendly human foods. With just a few teeny bits of leftover meat, a couple tablespoons of warm rice, a splash of chicken broth, etc, she so is excited and grateful for a delicious feast!