Again cows don't emit completely new gas into the atmosphere; all gas they emit originally came from the atmosphere. So their emissions are not in anyway a problem, as it's really just recycled atmosphere.

You'd might argue that they change the composition (eg changing it to methane gas), but methane also breaks down in the stratosphere. Sure it takes like 100+ years to happen, but it's temporary. You can set a population of cows, and keep it steady, and the amount of methane and other greenhouse gases in the atmosphere attributed to the cows won't change after some period of time. Now, growing the population of cows will grow this temporary store of gas, but cows bodies also are carbon sinks themselves which offsets it somewhat. And likewise, as you cite, reducing the population of cows and livestock would decrease their temporary contribution of gas. But this temporary store of methane isn't the root of our problems.

The real problem, is taking carbon from underground, and burning it. For nature to naturally reverse this process, takes millions of years. The only real solution is to stop burning fossil fuels, and/or to reverse the natural process faster somehow (like by repeatedly burying trees and growing new ones).