Perhaps have the romantic nationalism of 19th Century Germany focus more on the Holy Roman Empire, and in particular build up a myth about the election of the Emperor being some symbol of German moral superiority, such that a united Germany, be it Kleindeutschland or Großdeutschland, is almost forced to adopt an electoral system modeled on that of the HRE. Possibly with either multiple votes given to some electors based on the state's population, thus ensuring Prussian victory, or a tacit understanding that the Emperor must be of the House of Hohenzollern. Easily enough accomplished, if the requirement that the vote be unanimous is also carried over. Even if all 23 or so sovereigns in the Empire are given electoral votes, and unanimity is not required, the threat of Prussia leaving and tearing the heart out of the Empire, or even just being a pain in the arse, would bias most electoral votes towards the King of Prussia, just to keep things running smoothly, unless the Prussian king is very much unsuitable and another monarch in the Empire is a viable alternative.
Interestingly, in this scenario, one would expect Emperors to carry over the regnal numbers of the Holy Roman Emperors, rather than the Prussian kings. You'd have Frederich IV, rather than Frederich III.