Make its base quality dependent on the soil the Auroch or Mouflon spawns on (Or is on or however it works for hair ). I know logically one might be thinking soil != meat??!!! However, the way I see it these fucking animals would probably be eating grass or whatever out in the wild and grass is on soil and soil has quality so ya that's my logic.
Would make them not completely useless to people who have cows and sheeps of better quality for meat which doesn't take very long.
You did it for hairs and you can do it for meats!