Love this kind of 'napkin math'!
My family bought a quarter cow last January and we are almost all the way finished with it. So 1/4 cow over 8 months divided by the four people in my family equals about .78% of a cow per month per person in my family.
Multiplied out over a year, that would be ~9.4% of a cow per year, which is pretty much on par with your calculations. Nice piece!
Our cow was grass fed, grass finished on my dad's farm in upstate NY. Still a contributor to greenhouse gases etc, but better than the factory farmed versions in the grocery store and at restaurants.