The Prussian scheme is a pretty popular what-if, but I'm wondering what series of events could lead to the United States accepting a monarch. Frederick II supported the Patriots, but with the start of War of the Bavarian Succession, Fritz needed to be careful with Britain, not recognizing the United States and refusing their ships from Prussian ports. Would the war never happening have perhaps allowed Frederick to give them a bit more support?
Let's say Maximilian Joseph doesn't catch smallpox, delaying any crisis over Bavaria for a few years. Frederick decides to send a small force of Prussian regulars to America under the command of his brother Henry. Frederick was quite annoyed with his brother's attempts to get a crown for himself among other things, so I think he would be fine sending his brother off.
Henry famously never lost a battle during the Seven Years War, would he do as well in America? Assuming he does, he could easily become a figure like Lafayette, von Steuben, or Pulaski. It may require killing off Washington, but if the war still ends in the rebels' favor, this may be just enough for Henry to get himself a crown.
Is this scenario plausible, or would another be better?