By "hot" on the chicken, do you mean from the TCM perspective? And, does the lady think red meat "eats" the joint because of the inflammatory effects some meats have shown in humans (I think this was in context of auto-immune type situations, however)? If that's so, then chicken is also usually included in the inflammatory category (and actually even higher on some scales than red meat), and dairy is almost always considered super bad (some say even goat milk, despite it being low-to-no casein). The typical anti-inflammatory line of thought eventually leads one towards vegetarian/vegan diets, at least for humans. But, in dogs, I thought they've found that most plant oils can be highly inflammatory, especially when compared to animal-based fats. Can't win!
I'm not really updated on commercial foods, but I do wonder about the using senior (or non-puppy) formulas on a puppy—because dogs have different (i.e., more than just caloric) nutritional needs at different stages of life (the mineral requirements shift quite a bit as they age, IIRC), and I kind of worry that he'd be off-kilter in something or another if you choose a senior diet. However, I seem to recall that commercial foods are way over-supplemented anyway, and that the only difference among puppy/adult/senior foods tend to be caloric—so, if both of those are true, it maybe not be such a big deal? (I am guessing the fish weight management one you're considering is for adults?)
I wonder if you could specify what your goal is—like, reduce inflammation, suppress growth (not sure how one does this w/non-custom diet without creating other deficits), promote this and that—that might make it easier to prioritize what kinds of ingredients you choose for what purpose. Kind of as a side note, some people (usually western herbalists) rely on foods with mild, natural diuretic properties (say, burdock) as an important component of anti-inflammatories (they can help flush out byproducts of inflammation), too.
Sorry not much specific help!