Besides, the low residence time makes its contribution proportional to the rate of emission, instead of the total emitted (like CO2). That makes human-emitted methane a much easier problem to solve: if you start fighting it, the problem reduces. So, again, unless it's a large problem, it's not worth ignoring other sources to focus on it.
So, yes, coal is most of the short term problem, and nearly all of the long term problem. Coal is also the only one available on enough quantity to become a catastrophic problem. It's also a hugely disproportionate problem at the local level. It is also the one with worst economic ramping-down possibilities. Coal is the problem to solve, and if it requires increasing our methane emission by some less than 100%, it is still a non-brainier.
(Of course, on the next decades we will have to replace oil and gas by renewables anyway, or go without. And the sooner we do that, the better. But if it takes the focus away from coal, it better wait.)
I don't think I have seen any climate change research that say we can reach the goals and increase methane emission. If anything most seems to say that we need to reduce both CO2 and methane. Call me very skeptical to the claim that we could increase out methane emission by anything near 100% and still manage, but I am open to see sources.
I can't find a clear source for worldwide emissions, but every site I can find [1] [2] makes methane responsible for around 10% of the total heating. Because of the short life, doubling the emission rate would make it responsible for much less than 20% of the total heating.
The choice of focusing on 80% of the problem or 20% of it is a non-brainier. Now, I have no idea if it will satisfy your goal.
[1] https://www.epa.gov/ghgemissions/overview-greenhouse-gases
[2] (This one needs some calculation) https://undark.org/2019/05/13/methane-global-warming-climate...
> but at 28 times the effect of C02
By the way, it's more like 200 times (so 20000%). It is still not enough to focus on.
Sadly, the science is not that simple. When calculating the green house emissions from natural gas we also have to include methane leaks during production. Depending on what numbers you use, around 30% of all methane emissions in the US come from fracking, and methane is 28 times worse than carbon. Combined the methane and carbon dioxide from natural gas is a bigger contributor to green house effect than coal.
Of course coal is still very bad. If fracking contribute about 30% of the methane emissions, coal mining also contribute by around 9% and coal energy plants release about twice the amount of carbon in the air compared to natural gas.
The numbers also get a bit more complex if one consider short term vs long term climate change. Methane residence time in the atmosphere is much shorter than carbon dioxide, so after the current crisis of climate change the pollution that burning coal causes is harder to remove than natural gas. The damage however from climate change can be harder or impossible to fix, so its not a clear cut which of natural gas or coal is worse for our current situation.
Best is just to keep both in the ground and use hydro, geothermal, and nuclear as base load and supplemental wind/solar for industries that can take advantage of variable energy production.