The Jagellions might work as a dynastic route - considering they had Poland, Bohemia and Hungary - they could attempt to become HRE, and then King of France.
Alternatively, a Danish HRE could do it, specifically a Kalmar Union HRE. If the Kalmar Union can hold together, it can make further marriage alliances within the HRE - to the point of getting Elector-ship, or Electors on side. Italy would probably break off, or fundamentally ignore the HRE/a member being given some sort of title to grant them authority over Italy. At which point you have an HRE politically centred in the North - with the resources and logistics to take on and over Poland and the Baltics, and the ability to economically isolate Russia - and later invade France. If this HRE was light-touch overall, it could eventually reorganise into a Federal Empire.