- As said, you probably need to get rid of Italy sooner or later. But the trickery is that Italian title was one of the "markers" of the Empire.
I would see rather well a King of the Romans being distinct from the Emperor since the XIII century.
Seeing how Italy was divided, its pretty safe to assume that the King of the Romans would have as much power than the King of Arles pre-Imperial acquisition.
- Dynastic stability : After the XII century, HRE became a musical chairs look alike. In a era and place where stability of a state was directly dependent on the stability of the dynasty in place, that was really detrimential. Of course, it's a dialectic relationship but generally, more the dynasty is in place for a long time, is acknowledged and is not really challenged in his power, the more strong the feudal state is.
- Limit the ambitions of the emperors : it's kind of related to the first point. The original power of the HRE was in the maintenance of a public land : thanks to eastwards expansion, the german kings and the emperors could give away lands and ensure the service of nobles without damaging their power.
When this expansion halted, tough...Well it didn't really halted, but wasn't made at the benefit of HRE and the settlement of XII to XIV centuries beneficied more to his vassals and even rival states.
HRE didn't managed to maintain his interests everywhere : Italy, Papal States, Mediterranean, Baltic, Central Europe. They didn't had much choice for select their priorities, so it's why you should "help" them.
No Italy (except Frioul, in order to keep an eye on Southern Central Europe), no Burgundy, but keep Lotharingia, it's one of the main part of HRE regarding demographic and wealth.
With these three points, you somewhat helped the HRE to reach what you search : it would be still plagued with important vassals and little statelets, but you can't have everything.