Methane traps far more heat than CO2 before oxidizing back into it.

That doesn’t change the fact that you’re selectively counting only one side of a closed loop process. Methane may be a more efficient greenhouse gas than CO2 but if that effect dominated, we would expect to see the global warming trend start with the evolution of ruminants, not the Industrial Revolution (a time when the North American ruminant population actually declined a significant amount!)