"water vapour re-emits in all directions, not just up"
The same applies to Methane and CO2, the CO2 frequencies are close to saturation point, they never will be completely saturated but having little effect now. Methane has a short life in the atmosphere and breaks down to CO2 and water. Much of the Methane from livestock is absorbed by biologically active soil and is turned into humus. The same applies to methane because there is nothing much getting through the water vapour.
Take water vapour away as in the desert and you find that these other greenhouse gasses have little effect as you freeze at night
If you want to reduce CO2 running livestock is the best way of doing it and you can restore degraded carbon depleted soils as well
