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.
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.)