What would be the route to centralisation? A customs union? Common imperial army? Hereditary succession? Could all of these be done with a Reichstag majority vote?
It would be gradual, hereditary succession is not needed, defeating Prussia in 1740 avoids the whole mess that was the WotAS, so the hereditary succession of the House of Habsburg is maintained. So yeah, more political consensus, more participation in the Perpetual Diet to organize the Empire as some workable entity, a common army is out of question unless all princes but Austria are trashed and the Habsurgs end on top (like some Napoleonic war), but even so it would face foreign opposition (if not France the British Hanoverians), so expanding and, most important, consolidating Austrian influence over the princes (at the expense of powers like France, Sweden and Denmark) could establish of sort of "Commonwealth" where the HRE is seem as unified, but tenuous in practice, but in any scenario some sorts of revolution that breaks the political theory of the day (like the French one) is necessary to break the status quo, should the event unfold like OTL, Austria would be the only German power to emerge victorious, and the newly restored entity (a HRE or the German Confederation) is more unified under the whims of the Habsburgs.
For the "could it be done with the Reichstag" the answer would be yes if the circunstances allows, and no if otherwise, simply put the HRE didn't have a coherent "constitution" to be called for decision, rather the traditional laws of the Empire were always based on interpretions that suited the involved party, in the end you could do anything to the structure of the Empire there, however it depends on the political strenght of the party interested in those changes. As a political scientest in the 17th (or was it on 18th, I don't really remember) century said: "Germany is ruled in the German way"
The whole point of the HRE was that it was meant to protect Interests and Privileges; a centralised nation-state apparatus would defeat the point.
I would disagree, but not entirely, the HRE simply didn't have "a point", the prince definitely liked the interpretation of the German liberties, but the Emperor could argue that those liberties needs a strong government to be protected, the HRE in the 18th century doesn't need to be a French-like centralized union, an example for this would the Maximilian's Reichreform, it did create a, questionable, workable system with Imperial Circles and etc.