'Okay there's a few important aspects to look at here, this religeous split hasn't made the Emperor weaker, it has de facto made him stronger, a weak Pope means that the Emperors control over the rich and powerful ecclessial estates/states in Germany are extented. The ecclessial rulers was often from the Imperial Knightly families whom even in OTL with lots of them being Protestants was strong base for the Emperors support. Here where they belong to the Imperial Church, and the Emperor has more control over the ecclessial estates, he's more free to reward them with positions and copntrol of those estates, and they make a even stronger base for him.
The clichee about the defragmented HRE are as I said a clichee, the Germany was by the standards of the late medieval periode a unified state, yes the princes/nobles had lor of power but so did they in lot of others European states of the time. What killed the HRE in reality was the 30 Years War, which de facto removed the vassal bond between the Emperor and the greater princes.
The next important aspect to understand are population size in 1500 Europe had between 48 and 70 million inhabitants, the entire Arabic (not Muslim) world plus the Ottomans possesion had less than 15 millions*. France had a greater population than that (16,4 million). In OTL the Ottomans failed to move beyond Hungary, while the Emperor had to fight both the French, the Pope and the Protestants in Germany. I don't see why they would have greater succes here, where the Emperor can use the weak position of Ecclessial power to extent his control and influence over Germany (and Italy).
I know that many people think that the Ottomans could conquer the entire world, and it only because they didn't want to they didn't, but in truth the problem was that the Ottomans was at the absolut border of what they could conquer, if everything goes well I could see them extent their power to Italy, but that's it. France or/and Germany, there's no way in Hell they're going to succed at that.
The last aspect you forget are how Iberia are going to develop without a unified Church. In all likelyhood without a unified Church to push them to a increased intolerance, we may very well see them letting the Muslim and Jewish minority stay (through the Muslims will likely slowly be assimilated). Of course we're quite unlikely to see Columbus in this world, which will lead to a quite different colonisation of the new world. So we have a Spain which haveen't driven the mechant minorities out and doesn't have the great infusion silver, the result are likely that they develop a more fuctioning economy, people tend to forget that 16th century Spain wasn't a backwater, but one of Europes most modern states at the technological forefront, their colonies destroyed that by giving little incentiment to keep up before it was to late.
*of those around a 1/3 was Christians
Seconded. The Ottomans couldn't take Vienna in OTL, largely due to supply/logistics issues, so I just don't see them going much further no matter what the political situation in Europe is. Similarly, I don't see the Arabs regaining any of Iberia in the 15th century, unless the Ottomans help them out.
I hate to say this, DJC, but the only way you will simply delete European civilization after 1300 is to have a comet smash right into it. Your Papal Wars will result in a quite different Europe from OTL (most likely one with nationally controlled churches, and maybe an Ottoman Empire that gets slightly more territory), but European civilization will almost certainly recover and dominate the world like OTL.
The best you can do without involving ASB's is to have one or more POD's in the 11th-13th century that prevent the fall of al-Andalus to the Christians, and have some POD's in Chinese court politics that produce a Chinese government more favorable to exploration, and which eventually explores the Pacific coast. That way, American colonization will be a competition between three different civilizations-European, Islamic (specifically, al-Andalus and maybe a North African country or two) and the Chinese.