Look, Hitler, while not what you would call a practicing Catholic, did have a positive view of his childhood religion. According to Albert Speer, he was disgusted by Himmler's neo-Paganism and actually tried to talk Goering and Gobbels out of their anti-clericalism.
Speer did go on to say that Hitler did have a good opinion on the head of the United church of Prussia at the time, and would have been fine setting him up as head of a unified German Christian church, but wasn't in a good position to do that.
Based on this, the aforementioned positive relations he had with Islamic leaders, and what is known about Hitler's psychology, I think that the following conclusions can be drawn:
1. As disturbing as it sounds, Adolf Hitler believed in God.
2. As even more deeply disturbing as it sounds, Hitler believed he was doing the will of God in uniting the people under his rule and weeding out the weak and evil (and I don't even want to think about what toxic brew of Christian theology, Nietzschian philosophy, Wagnerian opera, German nationalism, and plain old Anti-Semitism he drew that from)
3. Hitler had a good understanding of the power of religion and spirituality in people's lives, and how that could be used to motivate them (this is the master of pathos we are talking about here, and you really can't argue that there wasn't a cultivated religious aspect to his rallies)
4. Hitler had an overpowering urge to unite anything and everything he touched into a hierarchy overseen by a powerful leader. Dissent was intolerable to him, and control was paramount. Based on this, I suspect (but cannot prove) that he felt most attracted to Catholicism and Islam because of their strict hierarchical structures (remember now that the Ottoman Caliphate had only collapsed some 20 years prior, and none of the successor states had yet built up their own factions into the sort of jostling branches of Sunni Islam we see today, so it would have looked a great deal more hierarchical then)
5. Since Hitler wanted a united, hierarchical faith for his Germany, was born a Catholic, had his power base in Catholic South Germany and Austria, planned to dominate Italy into junior partner status, favored dramatic, baroque ceremonies and architecture, and liked to think of his Reich as the restoration of the Holy Roman Empire, I strongly, strongly suspect that his long-term goal on the religious front was to bring the Papacy under his thumb and unite Germany and Europe under a Nazified Catholic Church. He may have created a Caliphate too that took orders from him, but I almost suspect he might have gone full crusader and tried to get back the Holy Land for the glory of his religion (and I mean his religion).
Because of this, I really can't see him converting to Islam as it would contradict too many of his desires, despite his sympathies for a faith that emphasizes the concentration of secular and religious power in a single individual.
Now, if you will excuse me, I need to go take a shower. My skin is crawling too much.