While I'm wholeheartedly agree with most (if not all) of your arguments, Eurofed, there are still some problems about East-West division of the Empire...
The western (or northern, in this ATL) part will become increasingly Germanic (or Slavic, or even Nordic), while the eastern part will become increasingly Hellenic, or even Persian in nature...
The West also more sparsely populated and have less wealth than the East, thus sharpening the division...
Is there any effective way to solve this problem...?
Well, as a matter of fact I do recognize that while with these borders, the OTL political and cultural fragmentation of Europe is way implausible, there still is a substantial likelihood that during a dynastic cycle or another, Rome might get permanently divided along the East-West split. The Latin-Greek fault line was apparently enduring and it might be the basis for an enduring division. Nonetheless, Rome showed a very strong political and cultural self-identity that crossed the linguistic division, so it is also quite possible that the pull to unity is stronger than the East-West divide.
It could easily go both ways, in different TLs, depending on which butterflies one picks.
Some nitpicks: while the northern half is indeed going to be mainly Celtic-Germanic ethnically, linguistically it is going to be a Latin sea. IOTL Latin all but wiped out Celtic languages in Roman areas, and there is no reasonable justification to expect it would be different for Germanic ones. ITTL Germanic languages would only survive in Scandinavia and quite likely in Sarmatia thanks to the migration of Gothic tribes (ironically, Latinization of Germany most likely means Germanization of Russia). Likewise, while the eastern half would be an Hellenic-Egyptian-Semitic-Persian ethnic hodgepodge, it would be a Greek sea linguistically. Persian might or might not become and remain a significant Imperial regional language (although its long-term ability to withstand replacement by Greek is rather questionable) only if Rome eventually goes and conquers Persia.
As for relative wealth of the two halves, it is true to a degree and for a time, but over time the balance is going to evolve towards parity, especially with the addition of Germania. Europe in a successful Rome cum Germania is going to skip the Dark Ages economic and social collapse (China shows that dynastic crises of its sort were bad for society but nowhere that bad) and immediately progress from the early Imperial period to the equivalent of the High/Late Middle Ages without feudalism and without a technological gradient with the East.
I'm thinking with so much more territory, the eventual division of the empire would come even sooner then it did OTL. Perhaps the 3rd century would not see a re-unified Empire, but rather a permanent Gallic-German Empire and and a permanent and much larger Palmyrene Empire?
