In fact, it's the situation after Merseen and Ribemont-like treaties
Verdun-Like
Pippin : Aquitaine + Burgondy + theorical authority on Hispania
Charles : Neustria + Frise + Austrasia
Ludwig : Saxe + Francony + Swabia + Bavaria
Lothar : Lombardia + Frioul + Carinthia + Benevent + Imperial title
Lothar have better territories, but as they are too many opponents, no one can endure perpetual war and differents alliances. So his brothers just wait Lothar's sons blow up his part.
Pippin have a prosperous territory, but rebellious too, in fact 1/3 of his part avoid his rule. (Hispania, Gascony,
Charles, thanks to his father support (at his death) keeps the heart of fraknish empire
Ludwig have forces, many support in noblity, but his brother didn't want to make him too powerful, so Germania
Merseen-like
Pipin II : Aquitaine + 1/4 of Burgondy
Charles : Neustria + Austrasia + Northen Burgondy
Ludwig : Saxe + Francony + Swabia + Bavaria + Carinthia
Lothar II : Southern Burgondy + Lombardia + Frioul + Theorical authority on Benevent
Lothar dies, parting his kingdom in two (Carinthia/Frioul / Lombardia + italy) but the war between his sons make carolingians follow this exemple. Pippin II, allied with Karl, loose, and lost most of Burgondy.
Ludwig takes Carinthia, Charles Northen Burgondy, but loose Frise (to Ludwig)
Lothar II became the one ruler in Italia
Ribemont-like
Pippin II : Aquitaine + 1/2 of Burgondy
Charles's sucessor : Neustria + Frise + Austrasia + 1/2 of Burgondy + Lombardia + Frioul
Ludwig's sucessor : Saxony + Franconia + Swabia
Bosson (proclamed himself king) : Bavaria + Carinthia
Lothar II died, and Charles became emperor, taking all his kingdom, without Frioul and a part of Burgondy.
War in Germany, and, Bosson declares himself king of Bavaria, Ludwig sucessor having : Frise + Saxony + Francony + Swabia + Frioul
Future planned :
Aquitaine : Became a little kingdom, without any great hope of expension in Europe, maybe in Peninsula, and will be more or less linked to HRE
HRE : (1)More Western centered, and very soon spilted in many states. Carolingian dynasty periclites, and because of it, of norman attacks and situation, Francia Avoid HRE rule and became independent with a Robertian -like dynasty.
HRE survives in Italy, in a very very formal way, having Aquitaine, Italy, Bavaria, but not very more, until an Otto-like dynasty (maybe Toscan)
(2) Surviving HRE in Francia and Italia, more decentralized than OTL. more possibilities for italians to avoid imperial authority, and micro-states in Switzerland and Alsace. In France, Robertians are powerful, but they are just one of the 4/5 greats lords in the country.
Germania became a strong kingdom, controlling northen tradeway
Maybe it's more logical in this way?
Map in 890