Avoid the Vasas at any cost.
Well, I don't think its necessary to go that far back...just prevent the Deluge. One idea I had in that direction...from what I understand, when the Polish monarchy ruled Ukraine, they recruited army units of Cossacks (Registered Cossacks, I think they were called). It was also my understand that most Ukrainians/Ruthenians, Cossacks included, were opposed to the landowning Polish gentry, who in turn were opposed to the monarchy getting too powerful.
So...is it possible for the king to turn these two against each other? Say, by guaranteeing religious toleration, and possibly some personal freedoms, to the Ukrainians, and recruiting lots of registered Cossacks. When the nobles get fed up with this and rebel, the monarchy now has plenty of cossacks to add to its loyal troops, and is thus able to crush the rebellious nobility, confiscate all their estates, and reassert royal power (get rid of the Liberum Veto, and maybe move towards making the crown hereditary). Then 18th century Poland can construct a modern army of drilled and trained musketmen, augmented of course by Cossack cavalry (I think maintaining whatever religious tolerance the Orthodox got in the first part of this would be in the crown's interest-it makes an Orthodox rebellion less likely, and somewhat dilutes the power of the Catholic church).
Another idea I had was that the Jagallion line survives longer, say into the Protestant reformation, and one of them converts to Lutheranism, allowing the state to both confiscate church property and centralize the church and education system under its control. (Plus, I seem to recall Imperial Russia having far less problems with its Lutheran subjects than its Catholic ones...perhaps the reverse would be true as well?) Eventually, of course, the Jagallion line goes extinct like OTL, and something like the Union of Lublin results in the (Lutheran) PLC forming...
So, does either of my ideas sound remotely plausible? I admit that they're kind of half-formed, and there are a lot of poeple here who know more Polish history than I do.