> then total atmospheric carbon is unchanged but the proportion of methane, and therefore the total GHG effect, is increased at that time. Summing over time, and you get an increase in overall heat that has been trapped
This is not correct. We are already in a steady state. Methane levels due to cattle are already at their maximum (given a fixed amount of cattle).
At any point in time, gras will absorb some CO2 from the atmosphere, cattle will convert some gras / carbon into methane and emit the latter into the atmosphere, and some methane in the atmosphere will decompose into CO2. This is a continuous process, that's happening every second, and if the amount of cattle is kept constant, there is a maximum amount of methane that you can reach in the atmosphere as well as a maximum amount of CO2. After all, the total amount of carbon involved in the process is constant – energy conservation dictates that mass doesn't appear out of nowhere.
In fact, since we've been doing agriculture for a time much longer than the time scale in which grass grows, a cow digests grass or methane decomposes into CO2, this whole closed loop has already settled into a steady state: At any point in time, the amounts of methane and CO2 in the atmosphere due to cattle are constant. The resulting radiative forcing will thus stay constant, too.