If they defeated the nobles, freed the serfs, and allowed freedom of movement, then they could send Polish settlers across the empire. However that is a pretty tall order.
Didn't those Poles become Ukrainians OTL, as in the guys who gave Bogdan Khmelnytsky/Chmielnicki his strength to beat Poland? That might be controlled if Poland had a policy like Russia toward dealing with the Cossacks--either your friends or foes in the borderlands, it seems.
To answer the OP, linguistic issues weren't an issue for strength and stability. As far as I know, didn't the idea of "Lithuanian" during Poland-Lithuania refer to what we now call Belorusians, i.e. Slavs? Or at least the whole "Old Ruthenian" language? It seems obvious to me that Poland-Lithuania needed a dictatorial/absolutist/authoritarian ruler as brutal as Ivan the Terrible and Peter the Great (both horrible yet strong and important individuals) combined more than any linguistic/ethnic sort of stuff.
Baltic languages might still survive anyway. Even if Vilnius was majority non-Baltic Lithuanian speaking, the peasants still spoke it, the Russian Empire couldn't stamp their language out, and there's always the Latvian language and variants for Baltic tongues, mostly under Swedish rule OTL. Any smart Polish ruler (I know, insert dumb "Polack" joke here, but still...) knows the future lies in the Ukrainian steppe and not the Latvian coast, so Poland-Lithuania can ignore OTL Latvia for the most part and focus elsewhere.