I was contemplating/had tried my hand at modding early feudal mechanics, specifically adding an early feudal government and stuff. I also was considering reworking the HRE to try to model the chaotic situation in the post-Carolingian situation. Specifically I wanted to make the HRE have a system distinct from the imperial decay mechanics, which do not make sense for it at all (unlike the Abassids or Byzantines) as it did not possess a real imperial bureaucracy or capital in this period.
The rough outline:
an early feudal government which must exert taxes through decisions, and calls its vassals to war, and is allowed to raid (and also moves its capital every ten years and has a slight demesne boost/increase to cost in building settlements, to try to reflect the itinerant monarchy of the period).
-an imperial decay like mechanic called majesty, which is tracked per ruler rather than over time, reflecting said ruler's ability to assert control over their vassals. It is set on accession by a combination of traits (strong, skilled warriors being better), crown laws, and dynasty, and affected over time by things like winning or losing battles, gaining prestige/piety, or being excommunicated. This in turn ties into other things, like requiring you to expend majesty to levy a tax on your feudal vassals via decision, or having said vassals try to invite foreign claimants if the king is weak (as happened repeatedly with Italy) or else elevating a separate anti-emperor; I would also add an event to try to crown a co ruler, as happened historically with various monarchies (including the HRE) as a potential path to de facto and then de jure centralization. The Pope, ideally, should have a massive impact on these relations, as they did historically, with an ultimate goal of trying to depict the Investiture Controversy (unfortunately the pre-investiture controversy fact of the Pope being generally appointed by the Emperor- or rather, being both appointed by him,. and approving/appointing him a la Charlemagne, is not something that can be easily modeled, especially if I wanted to say, use a Nicene Christianity pre-schism and then have them split up via event.
In regards to the HRE at game start there would be a de jure Carolingian Empire held by Louis II encompassing all of Charlemagnes Empire. All Carolingians (or de jure king vassals) have a permanent claim/casus belli against the emperor. Whoever is King of Italy/Lombardy would be able to petition the Pope for the Imperial Crown; not possessing this title would have a massive penalty to majesty, weakening the kingdom and making it much more likely for the king to be deposed or invaded.
I would also like to consider restricting or revamping forming lesser titles in the HRE- duchies should not be formed willy nilly, as their formation was (historically at least) a reflection of the development of feudalism and the disintegration of regional "stem duchies" into more formally delineated entities; this fragmentation was as much a refinement or reassessment of Imperial/Royal power as a weaking of it, indeed it often was used as a weapon by the emperors to strengthen their power (so for instance Bavaria lost Austria, Carinthia and Verona, and Spoleto was split off from Tuscany, both intended to weaken an overmighty vassal).
Italy itself could have at least one alternate Empire formable- assuming an independent Italian monarch which has max absolutism and control over Rome they could reform the Western Roman Empire. In a scenario where Italy had maintained her independence and centralized successfully it is exceedingly likely that the Italian monarch would have tried to reclaim that title, especially in a pre-Ottonian Europe.
More generally perhaps reworkingde jure formables is not a bad idea, albeit it is somewhat murky- while something of a shadow kingdom it would be too far to argue that there was not a sense, post-Charlemagne (or even pre-Charlemagne), of "Empire" encompassing the west, especially in regards to Italy herself. Whether that would be an Ottonian kingdom or something else, post 800 there was almost certainly going to be a "Holy Roman Empire" of some form or another, even if said empire was based entirely in the Italian Peninsula or out of France or Burgundy instead of the historical union between Germany and Italy. Nevertheless the current situation does suggest reflection, as the de jure setup (especially with the stem duchies being separate kingdoms... with titular duchies in their place) is awkward and belies the underlying difficulties.