I agree with you that Danzig in Swedish hands is very far-fetched - that is why I called it a pipe dream (but Sweden would absolutely love if they could get it and get away with it). Karl is smart enough to not go for it - OTL he forced the city to pay tribute and return the value of the Swedish royal treasury the burghers had "loaned" from Karl Knutsson (Bonde) when he fled with the royal treasury from Stockholm to Danzig 1457 (21 200 Prussian marks) in late 1703 but did not attempt to lay siege to it. As you say, Denmark, Brandenburg-Prussia, the Emperor, the Dutch and the English would all be pissed, and even with a Russian alliance Karl would not feel safe enough against such a potential coalition - Karl and other contemporaries would not view the Russians as able to poject power beyond Livonia, Estonia and the eastern parts of Poland-Lithuania. Besides, as I said, any Swedish-forced Polish-Lithuanian monarch would lose most if not all his legitimacy if he signed away Danzig.
I would like to play the devil's advocate in the matter of Danzig. I know you find it likely- with good reason, but hear me out.
My thesis is that the WoSS represents a unique strategic opportunity and the decision-making will be influenced by past experiences and current circumstances.
First of all, the strategic position of Sweden is completely different. An allied Russia means that the Swedes' calculation over the first years of the war will be quite different. It is true, in OTL Karl didn't go for Royal Prussia. However, there was a second front on his back, even after Narva. Under these circumstances, it would have been idiotic overextension to go for Royal Prussia. There is also no need to provide men and supplies in Livonia and Ingria to deal with the Russians. At the same time, these provinces are not ravaged by war and can provide food and taxes.
The ultimate dream of swedish policy was the control of the Sound and with it of all Baltic. They have learned a bitter lesson that the Maritime Powers will never allow such thing to happen. The next best objective is Danzig and controlling the Vistula trade. However, the WoSS will soon start. In the first crucial years, the arch-enemy of the Maritime Powers holds a line from Antwerp to Namur. A dagger held at the throat of both England and the United Provinces. It might be possible that the Maritime Powers despite their preoccupation in Flanders and the Rhine send their fleets if the Swedes try to land on Zealand. However, would they respond with military force over a secondary objective such as Danzig? I sincerely doubt so.
Would the Maritime Powers try to escalate the war and add a Great Power as an enemy? They face the possibility of having their perceived boogeyman controlling Europe from Antwerp to Naples. They will dislike a swedish move on Royal Prussia, but under these circumstances they cannot afford to make an enemy out of Sweden.
The response of the Emperor is of very limited importance. The Emperor has the French at the Rhine, a hostile Bavaria and Rákóczi's Revolt to deal with. Failure in the Germanies or Hungary might mean the loss of his House's position in Europe. At best, the Emperor will send a strong worded letter.
Therefore, for the Swedish policy makers it will seem as a golden opportunity. For all intents and purposes the PLC is neutralized, the Maritime Powers have a Sun King to fry and the Emperor cannot do anything.
But what about after the end of the WoSS ? I think we should make our calculations based on the knowledge they have in 1701. The Swedish policy-makers have spent their entire adulthoods watching half of Europe trying to contain France. And barely succeeding in every war so far. In their minds there are two blocks of power, almost equal that regularly clash. The recent war only stengthens this view. In this geopolitical landscape, where two behemoths crush against each othrr, smaller Powers can keep their gains if they play their cards smartly.
They also knoe enough of the political character of the Dutch Republic. They are merchants and fight to support their commercial interests. If they are presented by a fait accompli - swedish Danzig- will they go to war with Sweden after they dealt with France, just for honor's sake? They are burghers after all, no honorable aristocrats like the Swedes themselves. In any case, dutch ships would still arrive at Danzig and trade will continue to flow- it is the swedish interest after all. They need naval supplies from Sweden and Russia, they need grain from Danzig and Riga and the Swedes would be happy to continue trading. It would be something weird according to 17th century history, if the Dutch would stop acting as Dutch when resented with a fait accompli.
Lastly, Royal Prussia can produce a greater surplus to the swedish budget than Ingria. In OTL, when Frederick annexed it during the 1st Partition of Poland, the province - without Danzig- provided 1,7 million prussian thalers in taxes. At 16,7 g of silver per thaler, that is a lot of silver.
I don't think the Swedes will overly care about polish hostility to be honest. The PLC is facing a new Deluge and without Ukraine it will be perceived as a smaller power. The Polish magnates would still need to export their grain. After some time they would have to accept the new order, as they don't have the institutions of a centralized state to continue a very long war. Especially while having the Russians on their flank and they are open up to Cossack raids. Granted, the Russians won't be perceived as a capable army by the Swedes, but even cannon fodder has its uses.
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