Well, you gave it to the Brits and now it is too late to take it back so your grand schema of squeezing the Brits out of the Med is in a grave danger.
Well, they were also be moving Eastward so perhaps their ultimate goal was conquest of the North America.
As for the "dream", the arguments are not convincing. There is a long way from having ports on the Sea of Azov and ending the Crimean raids to the Russian territory to the conquest of Constantinople. Danube delta was a convenient geographic border and also allowed, at least in theory, to control a commercial traffic by the river (as I understand, in OTL the route was important for Austria). If you really paid attention to the pattern of the Russian conquests on the Black Sea and beyond, most of them were in a wrong direction: the Eastern coast of the Black Sea, Caucasus and the CA. Border on the Danube remained stable (with the minor losses after the CW which had been returned in 1878) for all XIX century even if during that century the Russian armies had been
twice within an easy reach of Constantinople. Actually, during the war of 1877-78 AII gave an explicit order
not to enter Constantinople.
The main and well-documented Russian interest was for the Ottomans not to let the 3rd party warships into the Black Sea.
Of course, I'm not trying to limit a flight of your imagination in any way (after all we are in alt-history)
but if you are
seriously insisting on that point, you have to bring up something more substantial than capture of Azov and Crimea.
Well, a strong monarchy with the powerful magnates is possible in theory but unlikely because, if the said magnates are sane, t6hey'll do everything in their power to curb the royal power down to a size which suits them, aka to make it as impotent as possible. The Polish-style monarchy is a perfect illustration of that pattern and Britain had been lacking the really
powerful magnates probably since the Wars of the Roses and those who left had been taken care of by the Tudors.
The key question is how powerful is a newly-created monarch vs. the magnates. The last Prince of Transylvania was
Francis II Rákóczi but he is long gone and AFAIK there was no unquestionably top ranking magnate family powerful on it own right, the Hapsburgs had been taking care of this. Some foreign potentate (who) may have an army of his own but I doubt that the newly-independent Hungarian magnates would welcome a foreign army more than the Polish magnates welcomed a Saxon army. Quite clearly, creation of a meaningful monarchy would mean taxation and a power grab by the central power: creation of an army means taxation and as soon as such an army is created and subordinated to the king, the aristocracy as a semi-independent class is gone. Happened in France, Russia and Spain.
I quite agree that a threat from outside can provide some kind of a stimulus for a reasonable behavior (it did not after the death of Mattias Corvinus) but in your scenario there is no clear and present danger: the Hapsburgs are almost powerless (and probably the Bavarian emperors and Kings of Prussia are going to help keeping them in check), the Ottomans are on an obvious decline and mostly in a defensive mode of actions with Russia being potentially available as an ally against them. The PLC is powerless, no matter who is its king, and can't fight an aggressive war without getting Russia involved.
Let's put it this way, the OTL threat from the Hapsburgs and Russia did not force them into the radical reforms until early XIX, which is well past your time frame. I have no idea how and when in your schema they are losing Serbian territories (unless they simply did not get back the territories they lost much earlier to the Hapsburgs) and I can
for sure that the part about the Russians of the XVIII century marching all the way to Sophia and Adrianople is a pure fantasy which was
technically impossible. The far end of the Russian logistics was
slightly beyond the Danube (below is the map of the war of 1768-74). To get any further you need the fundamental reforms of post-Napoleonic period and even then it was a risky shoe-string operation (in 1829 out of 100K+ only less than 25K reached Adrianople and the territorial acquisitions had been exclusively on the Eastern Coast of the Black Sea). In the mid-XVIII crossing just beyond the Danube was considered an unbelievable success.
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Notice that the Ottomans did not reform their army after 1774 when its tactical problems became obvious (defeat at Kagul). The Ottoman Empire still had a greater population than Russia and could master the bigger armies which was considered an adequate answer to the challenge.
Which "untapped resources" are you talking about? The PLC as a military factor proved to be something close to zero during the WoPS and its ruling class resisted attempt of the military reforms even during the reign of Stanislaw Poniatovsky. The
same Hapsburg would not be allowed to rule both Austria and the PLC and while ruler of the Rump Austria could potentially raise
some army, ruler of the PLC was going to have only the same few thousands troops as in OTL. The
union would not be allowed to happen by Russia and Prussia and the same goes for "circumventing any Russian-imposed limitations including the liberum veto" which actually was not imposed by Russia: to give credit where it is due, its OTL application was Polish.
The problem would be not only in the Russian reaction but in the Polish reaction as well: the reforms of Stanislaw had been backed by CII and resisted by the Polish Bar Confederacy. The same goes for some other issues: the Polish nobility proved to be quite self-destructive on the issues which they considered a matter of principle or religion.
But it is more or less clear that even if just by the reasons of geography the Bavarian emperors would be mostly concerned with the German and "Western" aspects of the politics: their territories are not really exposed to the "East". So the issues are going to be Bavaria vs. France, Bavaria vs. Prussia, Bavaria and the rest of the HRE, etc.
