Once you hit the quality cap for an animal (ie, q100 for deer) there's no possible way to raise the quality any higher on the hide, guts, meat, or bones. For domesticated animals, obviously, you can raise this higher through breeding. My idea is this:
For the following animals: Fox, Deer, Bear
Ignore the quality cap for meat.
I believe the current quality formula is: (cutting tool + animal quality) / 2 [hardcapped at animal quality]
As cutting tool quality improves so do the qualities of wild meat. Fox meat also becomes MUCH improved without a cap. This allows wild meat to still have some advancement in quality.
I don't think you need a cutting tool to butcher rabbits, but if the cutting tool quality would affect their meat too without a cap that would be terrific.
Animals such as mouflon, aurochs, chickens, and boars should keep their caps to continue to reward domestication. I believe domesticated animals should be the best source for quality hide, meats of their type, intestines, and bones since these animals are not easily "farmed" in the gaming sense.
As a side note, it would be nice if all wild-only animal products had their caps removed, but that's another topic. Rabbit fur and bear hide would be fine, but deer antlers and bear teeth could cause some imbalance with the current formula.