Just a few musings.
Berbers/Maghrebi cultures should definitely be raiding overseas like the Norse did, Vanilla gave them the ability already but HIP hasn't added it yet, and the Magyras also need to end up as the menace they were in the 9th and early 10th centuries. Additionally all the Carolingian kingdoms should probably be elective gavelkind in the Old Gods start... maybe add in the Kingdom of Provence/Lower Burgundy as well, with event and/or decision to reunite them if they are joined together.
Moreover duchies should ideally act like viceroyalties early on, gradually and inexorably shifting towards strict feudal succession by the 12th and 13th centuries. Dukes in the HRE were pretty much hired and fired at the emperor's will, their power based on holding extensive territories more than having a higher rank.
There could be some mechanic for western Europe/early feudal governments to model the fluctuating and non-institutionalized power of early medieval kings: let's call it majesty.
Majesty ranges from 0 to 100, defaulting to 50 with no effect. Like Imperial decay it increases/decreases levy size, vassal opinion, and army morale, but unlike decay it's mostly determined by short term events and the person of the king rather than institutions.
Majesty increases for having non-elective succession, being a relative/dynasty member of your successor, winning wars and battles (in person), having high crown authority, having high prestige, having good traits (strong, genius, brilliant strategist), and is hurt by provinces in the kingdom being looted or sieged, by losing battles (in person) or wars, being underage or female, having low martial/diplomacy/prestige, having a regency, getting excommunicated, increasing crown authority (as a temporary penalty parallel to the opinion penalty) or by civil wars or usurpations.
In addition to the penalty if majesty is low enough vassals can invite neighboring dukes/kings to seize the kingdom for themselves (as happened in Italy with Otto the Great, the Bosonids of Provence and Arnulf of Carinthia) and/or plot to usurp the kingdom for themselves, a la the Capets in France. The Pope should also be very, very active in Imperial politics, giving claims to various ambitious lords if he doesn't like the current emperor. Majesty could also be a cap for changing crown laws and revoking/creating titles, for instance. The HRE and Italy (as well as Burgundy and Lotharingia to an extent) aren't really modeled that well- even strong kings could and did face problems if the monarch's power was weak or they were unlucky enough to be raided by all of their neighbors.
In regards to the Old Gods, in place of the German-based HRE (which is somewhat anachronstic) I'd add a titular
Carolingian Empire held by Louis of Italy, with the Pope as his vassal, and an unformable "Carolingian Realms" encompassing all of the Karling kingdoms. "Italy" de jure encompasses all of the Patrimonium save perhaps Rome (and maybe also Corisca?), mainly to prevent a "king of the Patrimonium" forming from Elective Gavelkind, and also allows the Duke of Spoleto to both participate in elections and desire the crown
as they did historically.
Upon the succession of a new emperor all independent kings in the Carolingian Realms can either acknowledge the title or not; if any fail to do so causes the empire's destruction. From then on it becomes possible to reform the Empire, as either HRE currently in the mod, as a king of Italy who manages to overpower his vassals (as for instance in the excellent
Sons of the Harlot Empress timeline on Alt-History), or with a generic "restore the EMpire of Charlemagne" for anyone who holds/Controls Italy and has a large demesne within the Carolingian Realms; this will cause the HRE to form as it currently does, but only if the Pope agrees- the papal coronation was an essential prerequisite for the Imperial title from Charlemagne on through to the Habsburgs. Regardless of how it forms it should include Rome and the Patrimonium as de jure and de facto vassals, the former being "restored" upon the Empire's formation. In the 11th century, when the Investiture Controversy kicks off, the Pope should (usually) break free, gaining independence, taking the Patrimonium out of the de jure empire, and enforcing Papal Investiture; this would also presage republicanization and the Lombard League. The Pope's Support in the Lombard cities was a vital factor in their success; some sort of Guelf-Ghibelline system (with accompanying traits) to represent the varying loyalties of the cities.
In regards to the proposed urbanization event, the OTL kingdom of Italy went through more than a century of devastation, on top of the Gothic Wars and Lombard invasion before this, yet still recovered in time to become one of the wealthiest and most urbanized areas of Europe. IMHO some sort of tension between city and lord was probably inevitable. That said the communes eventually succumbed to despots- segnoria who established de facto (and in many cases de jure) hereditary succession- after the 11th and 12th century communes should come (usually) the despotism, perhaps a unique "Signoria" feudal government which can hold cities without penalty, created at the behest of the Emperor who elevates the lords to dukes.