The 34x potential I gave is for methane over a hundred years. https://en.wikipedia.org/wiki/Global_warming_potential
It's incredibly potent stuff, so much that despite the relatively quick breakdown, an initial mass of methane will have a warming effect that is 20-35x that of an equivalent mass of carbon dioxide over a century. GWP numbers take the brief half-life of methane into account when calculated. You're making the mistake of looking at the absolute quantity of methane and short half-life, and thinking that it couldn't possibly have much of an effect. Well, people have already run the numbers, and it can have a huge effect.
Current rates of methane leaks from mining natural gas could very well offset the benefits of moving away from coal: http://blog.nature.org/science/2016/06/24/natural-gas-coal-l...
Methane's very bad news, even in small quantities.
Anyway, your first link says " In the Fifth Assessment Report of the Intergovernmental Panel on Climate Change, methane has a lifetime of 12.4 years" (If that's X ln(2) for half life it's 8.6 years)
"This means that a methane emission will have 28 times the impact on temperature of a carbon dioxide emission of the same mass over the following 100 years." https://en.wikipedia.org/wiki/Atmospheric_methane
PS: As to small quantities, we are talking about billions of tons of a gas.
So if you use 34x that 1,000ppb is only 39,000 vs 124,000 meaning it's significantly less important overall contribution. It would need to reach ~4,347ppb to cause as much impact as CO2 has which is in nobody's projections that I have seen.
PS: "Methane has a large effect (24 times as strong as carbon dioxide per unit mole) for a brief period (having an estimated lifetime of 8.9±0.6 years in the atmosphere)" https://en.wikipedia.org/wiki/Atmospheric_methane So, if it's lifetime is ~8.3-9.5 years it's half life is around 1/2 that. However, I have also seen a lot of other numbers tossed around and most people want to make it seem much more important even if it's been rising very slowly.