With a POD in the middleages it is relatively easy for the Netherlands to consider themselves German; there was not much difference between what is now the Netherlands and what is now Germany. Cleves, East-Frisia and many other borderlands in Germany could easily have become Dutch, just like Groningen or gelderland could have easily become German if history was a little different. Although you have to remember the Netherlands has always been removed from the rest of the HRE, even during the Middle ages. It always has been more or less a backwater of the empire, a border area where the empire didn't have a lot of control and has been influenced by England and France. One of the most important counties and major influence of the Netherlands, Flanders, even was part of France (I realise most of Flanders isn't part of the Netherlands, but it was probably the most important part of the Netherlands).
As for other states, well, William III was a German noble (and the Dutch anthem says as much, dont try to deny it

). He was the eldest son of a count, but those lands by way of partition of inheritance went to his brother. If either line dies out quickly enough, the inheritance could come together again. In fact of course, the younger House of Nassau-Orange did until the French Revolution have some lands (half the Nassovian lands) in Germany. Of course, tiny Nassau isnt exactly what youre looking for I guess, that was more of an appendix of the Dutch stadholder
I do not understand who you mean with William III? The stadholder/king of England and the Netherlands? I wouldn't call him German. He was as Dutch as most Dutchmen and the Dutch anthem doesn't mention him. The Dutch anthem is about William "the Silent" of Orange. Who was of German blood being from Nassau, although I doubt that was meant by that line. I suspect they used Dutch/Diets/Duitsch in the meaning of "from the people" (or something like that), meaning that William the Silent was one of them; one of the Dutch people rebelling against the cruel Spanish oppressors. The Dutch anthem is a warsong after all.
And other German rulers - well there wasnt many German state at the time big enough to absorb the Netherlands. As with Nassau, it would rather go the other way round. Hm, maybe the House of Mark - actually the
United Duchies of Jülich-Cleves-Berg might be a good candidate. They were after all known to be religiously very tolerant, and sufficiently rich. And in any case, theyd be right around the corner, so to say. Of course, their ruler at the time, William V had lost a war against in the 1530s against Charles V over the succession in Guelders, and since then had avoided all conflicts with the Empire as good as possible. And besides, while it was a formidable German middlepower, in an European context it was a rather minor power of course, not comparable with England or France. So it would still be a poor candidate, just the best German one I can come up with...
I really don't think they are a good candidate. The Netherlands is just too strong and influential and those lands are just too culturaly and linguistically close to the Netherlands. If the Netherlands becomes part of Julich/Cleve/Berg/etc it would mean that Julich/Cleves becomes part of the Netherlands. The influence of rich Holland (anf maybe Brabant and Flanders) would be far too strong.
Now the Prussian scenario - I dunno. I think at that point the stadholder office wasnt yet hereditary, right? So pro forma the succession dispute was only about the Principality of Orange, which had been occupied by France anyways, so IOTL the conflict ended with the compromise that both sides could call themselves "Prince of Orange", without that title having any meaning. Oh, and Prussia got Lingen and Tecklenburg, of course. However, if the Prussian King wins the exclusive right to call himself Prince of Orange, then that would of course make him an obvious candidate for the stadholder office, since all stadholders (for the Netherlands as a whole) had been Princes of Orange. Assuming Prussia manages that, it could be the Netherlands and Prussia are indeed only united in personal union, with the institutions of the Republic remaining in existance and independant.
Hm, William III died in 1702. At that time the Prussian King was Frederick I, in fact the first King in Prussia, and that only since 1701, too. He was Williams cousin. Now, at that time he already had gotten what he wanted - a royal title for Prussia, as his price for Brandenburg-Prussias participation in the War of the Spanish Succession. Now that war was a major distraction for everybody in Europe, and everybody had that one goal to restrict French power. Of course, the Netherlands were a major part of the anti-French alliance. So Frederick I could not have simply invaded the Netherlands. Well, he could have, switching sides in the war, but that was just not his nature. Besides, it would have threatened the general acceptance of his new royal title. Now, if the stadholer-less Netherlands do something monumentally stupid that will see the rest of Europe welcome a Prussian intervention maybe... like if they consider switching to the French side in the war... then maybe... but even in that case I think the other anti-French powers and England especially would only accept Frederick I as stadholder, not as absolutist ruler...
I don't think Prussia would really work. The Netherlands was too rich and too independent. It already had its own identity at that time. It would be an influence on Prussia as much as on the Netherlands. All Prussian eastern territories, Lingen, Cleves, East-Frisia would become Dutchified (even more so than OTL). Although I always thought a Prussian-Dutch personal union would be interesting. Would they be able to form a union that was more Low-German in nature than German, would they just split because the Dutch and Prussian nature were so different, would Prussia suddenly be interested in recapturing the southern Netherlands?
That said, I don't think it will happen. The Netherlands can do without a stadholder. They did it twice and the moment it became apparent that the ruler of Prussia would try to become stadholder of (some of) the Dutch provinces, they would just refuse, or at least Holland who would force the other provinces not to accept him. They would just choose someone else who isn't as much of a threat (like the stadholder of Friesland like OTL) or just go without any (also like OTL).
Actually I think that after the treaty of Westphalia it will be extremly difficult to include a Netherlands that is willing to become German. From that point on the Netherlands existed as its own identity. Maybe you could even place it earlier at the pragmatic sanction, although at that point it could still become part of Germany (certainly considering it was directly ruled by the German Emperor). The only other ways I can see are just simply conquering and assimilating the Netherlands by Germany (which they never planned to do as far as I am aware of) or maybe the Netherlands being conquered by a non-German non-Dutch enemy.
Basicly my idea about that is Napoleon winning the Napoleonic wars and annexing the Netherlands and parts of Germany, while the rest of Germany forms Germany and opposes France. France tries to forcibly assimilate the Dutch and German parts, who try to resist (think Flanders in the early twentieth century). Germany helps the Dutch and Germans living in France, who see in them German brothers and after a war in which Germany defeats France, they all hapily join Germany.
BTW talking about weather Dutch is lower Saxon or low Franconian or whatever is irrelevant. There are no clear boundries in linguistics, at least not within a dialect continuum.