Other than Dr. Tims what other brands use chicken or turkey as major protein source with limited grains?
Grains limited how? As a source of calories or source of Protein?
Other than oats, whole grains that you would find in dog food are rather low in protein. Barley is a bit higher than rice or corn. Despite what you read whole corn does not have much protein, but it has some high levels of certain amino acids. Rice is rather low in protein.
Any food with 30% total protein without a vegetable concentrate like corn gluten, wheat gluten, rice gluten, pea protein, potato protein will have about 90% protein from animal sources. Foods with about 25% total protein will have about 80% - 85% total protein from animal sources.
I am assuming these examples have meat protein, fish protein and egg protein. Dried egg is very light and often shows up lower in the list but still provides very high levels of protein.
If you are looking for brands that are have low total carbohydrate and are good for most dogs, look at a traditional 30-20 plus or minus type food.
Dr. Tim's Pursuit & Momentum (Momentum has carb profile like Evo)
Eukanuba Premium Performance (excellent value & easy to get)
Native Level 3
Victor Hi-Pro Plus (excellent value)
The first too are more expensive on average, but if you can get Annamaet from a trainer, you will find excellent prices, like $1.30lb. Online, pricey but keep in mind Annamaet Ultra comes in 40lb bags, not 25,28,30lb bags.
Dr. Tim's on Petflow in 44lb bags is a real find @ $1.40lb no tax or shipping. Locally Pursuit is $1.75lb plus tax.
Eukanuba Premium is the easiest to get for most people and is a great choice.
So any on that list will have very low carbohydrate, if fact at or lower than Orijen. There are others that have more fat than 20% but I don't think they are good choices for most dogs. The only way to judge any of these levels is by calories. Higher fat foods with 30% protein will have about the same level of carbohydrate as most grain free foods. Just looking at the label doesn't tell you much because you don't know the weights of each ingredients and some ingredients are very light compared to what they provide, like egg.