Regarding post-Narva and the possibility of Swedish victory if they'd gone into Russia right away, I read that too. Then again, the question becomes
Could such a victory be sustained? If History teaches us anything, it seems to be Do Not Invade Russia.
@TheHandsomeBrute That's an interesting POD. And food for thought
Swedens number one goal, 1700-1702, was keeping to war outside of the Swedish Baltic provinces, which where still recovering from the massive famine ~1698ish (don't remember the exact date right off my head). The post Narva goal was, as I tried to communicate before, a similar victory against the Saxons and only then invade Russia. This was not achieved because the inablilty to get the cavalry over the Düna quickly, if they had been Augustus would have been force to face the Charles and most would have most likely lost.
I have seen a lot of threads and comments saying that Charles didn't understand that the Polish and Lithuanian nobles were neutral but as I understand it he did. It was just that he thought the diplomac root took too much time and believed he could either scare them into dethroning Augustus or dealing Augustus a quick decisive defeat forcing the noble too dethrone him.
--
If Sweden had finished the Saxon army in 1701 by the Düna river, Augustus would have been forced to sue for peace. He had no real army in the field at that point (I could be worng on that, he could have left some troops in Saxony). And once Saxony was out of the war there is only one enemy left, the Russians. The Russians who at that point would have nothing to through at you, they might be able to conduct scorched earth but Charles is closer to friendly terrioty and can much easier he resupied and reinforced.
If I where him, and had just forced Augustus out of the war, I would march on Novgorod, if it is burnt and destroyed rebuild it, crown a local noble "Prince of Novgorod" making a new smaller, easier controllable Russian state. I would march on Moscow, either the same year or next spring depending on the time of year, and burn/loot/destroy everything inside it.
If Charles is able to finish the Great Northern War before the conclusion of the Spanish War of Succesions he has to enter. One of the reasons for the British and Dutch help with landing on Sjaelland was the promise to enter on there side the upcoming war when his was finished with his.
--
If you want to read about Swedish Military Campaigns during the Great Northern War check out Warrior Dynasty. Half of the book is about Gustav II adolf campaign in Poland and Germany, the second half is about Karl XII campaign in the Great Northern War.