Well, if we're ever in a position where it's a realistic option, we simply offer him vassalage. Let him keep his territory and the prosperous little kingdom he's built for himself as a semi-autonomous Allied Region, but ensure that he ultimately pays his taxes to us, and that he does what we tell him to do when it comes to military operations. Make it clear that he's not getting a better offer, and that the alternative if he refuses is a full conquest where we do our level best to tear down everything he built and remake it in our own image after he's gone.
He already doesn't want Thrawn as an enemy now. Imagine how much more leery he'll be about the prospect of fighting us when we're the ones who clearly outclass the Alignment. But in any case, that's a problem for the not-so-near future, since we aren't in anywhere near a position to dictate terms like that yet. For now, cut trade deals, build ties, and just generally cooperate with the guy. Knowing Kaine, it's extremely unlikely that he'd be the one to initiate hostilities, so as long as we're making the right noises and not trying to pick a fight, he'll be a good neighbor.