If "eventually" is what's concerning you, then the 9-15 years timescale is of no use because there are many intermediate steps with many various processes and many sinks and many timescales, so there's no point limiting yourself to methane. It's a natural closed system.

I don't have the entirety of the various steps and loops in the carbon cycle in my head, I'm afraid, but I'd be very relucant to come to any conclusions based on an atmospheric methane timescale of 9-15 years and "eventually it turns into carbon dioxide".