Your best bet would be to not hobble them with an absurd constitution which made it impossible to ever do anything.
That and/or knock a few teeth out of Russia, putting laid on their westward intentions one way or another
Have the Dzungars badly batter or even conquer Russia from the East in the 17th Century when they are on their way up and pre-Peter the Great's "New Model Army". Poland-Lithuania becomes the frontline state for Europe and Christiandom against the heathen (Buddhist) Mongol horde if Russia is conquered or divided with Dzungary
What do you mean? Constitution was- of course- completely idiotic idea, but only because of neighbors who wanted nothing else but to eat Commonwealth. Or at least keep it weak. Without them, constitution itself was pretty good, regulating many things and curbing rights of magnates.
Aley is right. Ultracatholic Vasas didn't help it. Poland and GDL will be much better off as union of crowns as 95% of bullshit started when Jagellon dynasty ended and the Lublin Union happened, following by Brest Union which as implemented was just a thinly veiled attempt at spreading Catholicism to GDL, driving lower classes towards Russia.
During the war of 1654-1667 Alexis Miklailovich did pretty good PR presenting himself as the savior of Orthodox population, which given the massacre of Polotsk (for example) was pretty reasonable move for him.
Yes. It was quite a bloody time, as "Union" was brought at swordpoint and was seen as an intermediate step to outright conversion of Orthodoxes to Catholicism.