Honestly, it'd be better to just cut the head off and prevent the war in the first place. It'd help to not have a figure like Augustus II on the throne based on what I read up on about him. He basically neglected the state and dumped all of his focus onto his native Saxony. He also staffed much of the state with Saxons, which is always a brilliant plan to have a stable and effective government. Really goes well with the locals
. He also got preoccupied with expanding his realm and was a major factor in why Poland (and later on Sweden) would get their asses kicked by Russia. Essentially, he (and Charles XII to an extent) were major factors in why Poland got demolished, Sweden got weakened, and Russia picked up the pieces.
The best move really is to prevent his ascension to the throne. His desire to expand his family's power and the size of his realm got him dragged into a losing war after all. Failing that and you really want to keep the Northern War, kill Charles XII by having himself get killed at Riga. His decision to continue the fight as Augustus was begging for peace helped continue this long and nasty war. This also means that the main portion of Poland doesn't have to be besieged, since you know, Charles prosecuted the war. That also loses Sweden a good military commander though, so pick your poison.
You'd still need to get a better king than Augustus, since he basically will neglect Poland regardless. One that can preferably try and revitalize the state.