My vision of the HRE being united under a centralized monarchy with the Hohenstaufen house, starting with Barbarossa surviving the crusades, letting him, his longer living son, and this grandson (who possesses Sicily), centralize the empire into a hereditary monarchy. Italy is pacified after Henry the VI, who doesn't have to deal with the Welf rebellion thanks to butterflies from a longer-lived Barbarossa. The HRE centralizes over 5 generations and becomes hereditary, meaning it takes the path of France and ends up as an absolute monarcy. It comes to financially and militarily dominate its neighbors, France most of all. Italy remains quiet until the Renaissance and breaks away while the HRE is bogged down fighting France.
A reformation like event happens, but no dukes seize on it as a political tool for grabbing power. The Catholic church survives, moderating, mainly because no strong pope ever evolved, and doctrine is more maliable without a strong force opposing change. Catholism still is unified, though several off-shoots have sprung up that are oppressed by the majority. Civil unrest and trouble in the HRE as a result, but solved by decree from the strong monarch.
It is the dominant power on the continent and starts expanding East due to large population increases (18+ million by 1400's). Hiring explorers in the 1500's as part of the race to find new trade routes, new lands with gold are discovered, prompting competition with the Spanish, Portuguese, British, and French for exploitation colonies. The leaders in the push are from the Low Lands, who have a history of using the ocean for trade. Though a land power the HRE also has a moderate sized navy.