A division of Europe between the Bourbons and the Habsburgs

election of Poniatovski instead of Czartorysky was based upon the factors you listed taken with “minus”:
I didn't deny it. I selected all the "pluses" of Czartoryski as a things which could block him road to the throne in the eyes of Peter and Fritz.
I didn't deny it. I selected all the "pluses" of Czartoryski as a things which could block him road to the throne in the eyes of Peter and Fritz.
Well, they were pretty much the same in the eyes of Catherine (and Fritz). Needless to say that the OTL criteria proved to be far from optimal: in her desire to get a complete puppet Catherine ended up with a powerless candidate who kept causing problems. Well, while Catherine was definitely quite intelligent, her judgement of the people was not always perfect and superficial “brilliance” of her reign was camouflaging a lot of serious problems. It is not a big surprise that Paul initially was greeted by “everybody” as someone willing to start fighting corruption and wastefulness of the previous reign.
An interesting idea and discussion. @Comte de Dordogne, I agree that a Spanish POD would be the best bet. More specifically a surviving Joseph I. During the Spanish war Bavaria had sided with the Sun King and, as consequence, was occupied by Austria. Now Emperor Josef I planned to fully annex the Duchy when he formally placed the Elector Maximilian II Emanuel and his brother Archbishop-Elector Josef Clemens of Cologne under the Imperial ban. However, he was talked out of it by his advisors and pushed back any annexation to the end of the war. Unfortunately by that time he was dead and his brother Karl VI was on the throne. Karl was interested more in getting as much of the Spanish inheritance as possible and ignored Austria's position within the Empire, so allowed Bavaria to go back to the Wittelsbachs. So a good POD would be Josef I never gets measles and survives to annex Bavaria.

Second, to make sure that no one has to compensate the Bavarians, I think you should kill off that branch of the Wittelsbachs, which wouldn't be that hard. During the Measles endemic of the 1710s several royal families lost nearly all of their members, including the Bourbons (Louis XIV's son, grandson, granddaughter-in-law and great-grandson died of the disease, leaving only the future Louis XV alive), so it wouldn't be hard to handwave the illness to the captive Electoral family and kill the boys off. That means Bavaria can be annexed without need to compensate.

Third, sense you wanted a Bourbon in Naples and Sicily, I'd switch the fates of Josef and his brother Karl entirely, ie Karl dies of Measles and Josef never gets sick. This means the Spanish war ends for the same reason as OTL, the Habsburg candidate also being the Emperor and reviving the Empire of Charles V. Thus the Two Sicilies are left for a later Bourbon conquest.

Finally, to me, the best sequence of events after this would be a TTL Austrian succession war that sees Austria beat France-Prussia but not easily (Maybe First Silesian war goes to Prussia, but Austria wins the Second and perhaps kills Friedrich the Great in battle) and with little help from her Maritime allies (neither the Dutch nor the British sent troops to assist in Silesia?), Russia rise to more power than Austria wants on her border and France wanting to weaken Britain. It should set the stage for a TTL Diplomatic revolution that would create a rough division of what your wanting.
Perhaps the one way to do this would be to have bourbons in all latin counties - France, Spain, Italy, Sicily, etc. and habsburgs in all others - HRE/Germany, Austria, Bohemia, etc.