Although objectively it makes the most sense if we all eat less meat or even go vegan (in terms of bang-for-the-buck), from what I understand the methane problem is mostly a result of them not being fed a healthy diet.
Grassfed does not necessarily lead to more methane production, it depends on the mix of grass and secondary vegetation, on the grain mix being compared to, and on potential supplements.
Just reading the article you provided and
"Feeding high grain diets to cattle unequivocally lowers the formation of CH4 in the rumen."
seems to disagree with what you're saying?
Ah, you're right, it is a nuanced question. Perhaps more importantly: as mentioned in the (admittedly large) publication I cited, the rearing time for grassfed cattle is about 3x longer than factory farmed cattle, so the net methane output is considerably larger.
