I assume for your second option you mean:
Pogue howled out laughing with a gut-busting roar. Startled, Kae stiffened expecting to fight for her life.
“Po’, yawut Meircan? Un ats P-say wha pes. Welp, P-say Sowfilly style, Sowfee-say. As mi say, mi from ‘ere, mi ahways bint ‘ere. Mae’ say G-tahk fo Meircan,” despite Pogue’s outburst, only a few people around them stirred before falling right back to sleep. Unable to shake Pogue and unwilling to kill her, Kae was trapped. From there on in ignoring Kae’s pleas, Pogue jabbered away at full volume.
Not quite. I'd have it as
Pogue howled out laughing with a gut-busting roar. Startled, Kae stiffened, expecting to fight for her life.
“Po’, yawut Meircan?" Pogue yelled. [or called/yammered/whatever means loud] "Un ats P-say wha pes. Welp, P-say Sowfilly style, Sowfee-say. As mi say, mi from ‘ere, mi ahways bint ‘ere. Mae’ say G-tahk fo Meircan.”
Despite Pogue’s outburst, only a few people around them stirred before falling right back to sleep. Unable to shake Pogue and unwilling to kill her, Kae was trapped. From there on in, ignoring Kae’s pleas, Pogue jabbered away at full volume.
So the dialogue tag as soon as possible after Pogue starts speaking so there's no confusion. The "despite Pogue's" isn't actually a dialogue tag -- those are things like she said/cried/muttered -- it's the beginning of a fresh sentence, so needs to full stop (period) and capital letter. And although that line follows what Pogue has said/done, since it goes onto other things, to my mind it needs to be in a separate para of its own. (I wouldn't worry about avoiding short non-dialogue paras -- as long as you don't overdo them, they help to maintain pace and propel the story forward.)
I considered:
Pogue howled out laughing with a gut-busting roar. “Po’, yawut Meircan? Un ats P-say wha pes. Welp, P-say Sowfilly style, Sowfee-say. As mi say, mi from ‘ere, mi ahways bint ‘ere. Mae’ say G-tahk fo Meircan.”
Startled, Kae stiffened expecting to fight for her life. Despite Pogue’s outburst, only a few people around them stirred before falling right back to sleep. Unable to shake Pogue and unwilling to kill her, Kae was trapped. From there on in ignoring Kae’s pleas, Pogue jabbered away at full volume.
But, that's as wrong as the problem at hand; the order of events being:
Kae asks ?> Pogue laughs> Kae cringes> Pogue speaks> as Pogue speaks, Kae notes residents> Kae answers
I agree. You need Kae's reaction as soon as Pogue laughs, so it's much too late in that version. An alternative might be something like:
With a gut-busting laugh, Pogue roared “Po’, yawut Meircan?" Startled, Kae stiffened, expecting to fight for her life, but Pogue continued, oblivious: "Un ats P-say wha pes. Welp, P-say Sowfilly style, Sowfee-say. As mi say, mi from ‘ere, mi ahways bint ‘ere. Mae’ say G-tahk fo Meircan.”
But as I said before, you can pick away at lines in isolation -- and believe me, I do this all the time with my writing!! -- but the important thing is the overall effect of the whole scene/chapter. So leave this behind for now, and get on with the rest!