IMHO the best chance for the HRE to centralize was for Charles I & V to leave the Burgundian inheritance to the Maximilians instead of Spain.
This gives a the Maximilians a demesne that is roughly half of the HRE and by far the richer half. Allowing centralization to take place, especially with the legitimacy of fighting off the Turkish infidel.
Not really. Any centralization after the reformation needs one of two things to happen: 1. Either the Catholics crush the Protestants or 2. religion ceases to be a major political concern. That's why the Thirty years' war is really the only opportunity between the Reformation and 1700. It crushed the Emperor's religious and political rivals within the Empire and could have been the start of centralization if foreign intervention is avoided/derailed.
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I would go back to the 1500s and have the Hapsburgs adopt something between Anglicanism and Lutheranism. Quash the Catholics, establish a variant episcopacy, and place the Emperor or his pet as Head Of The Imperial Church.
Might backfire, but has a better chance of avoiding the effective north/south split the Reformation caused in the Germanies than anything else.
Not gonna happen under Emperor Karl nor would the idea ever cross his mind. Though I will say in theory it does have merit.