Any plausible conspiracy theory about N.II's death (in the residence of the Austrian Emperor) must include some mention of Franz II/I and his particularly nervous and suspicious nature. Anyone seen as posing a risk to the Monarchy would be dealt with. The Habsburgs were not simple Russians, the thought of using anything so crude as a window would be sneered at. If the threat had to be delicately dealt with, so as not to reflect badly on the Emperor, it would be carefully and professionally done: covering newspaper stories about poor health would be inserted in papers well before hand, a complete medical report detailing all necessary health issues would be compiled, and a proper death report filed.
There is a well known saying "The thanks of the Habsburg's" which translates basically into being stabbed in the back.
It's my understanding that the (post 1815) Franz II/I era was one of the more reactionary and ruthless.
Has there been any work on Franz II/I and the King of Rome? Which would on the surface have to be one of the more tortured relationships in history. And, after a quick look, it appears to have been exactly that; both Metternich and F. feared him getting outside of their reach. More than likely, F. began plotting this particular death from the first day of his coming under his control.
By all reports, Franz II/I was paranoid and delusional, he had an army of agents, spies, informers. If you want to know what F. was thinking about N.II, find the worst rumors circulating. If those rumors included N.II taking reign of some revolutionary uprising or even just a whisper of talk about there being a political role for him... his life would have been in danger. In addition, N.II's chosen military career would have been a strike against him. Would there have been talk inside inner Habsburg circles about a need of nipping this branch at the bud? Absolutely.
"Fatal Links: the Curious Deaths of Beethoven and the Two Napoleons, Altman puts forward the hypothesis that Beethoven's death was the result of deliberate poisoning on the part of agents of the Viennese authorities, at the same time drawing parallels with the deaths (by similar symptoms) of Napoleon Bonaparte and his son Napoleon II, the latter at the hands of the same Viennese authorities, by whom he was kept a virtual prisoner throughout most of his short life. Fatal Links draws exclusively on source evidence of letters and eye-witness reports and, while she was not privy to subsequent medical analysis of Beethoven's hair, her conclusions - that he showed symptoms of lead or arsenic poisoning - accord well with the result of the chemical analysis."