WI: Umayyad Caliphate conquers and reunites entire former Roman Empire, becomes Romanized?

This is a continuation of a small discussion on the Reverse the Fates of Rome and China thread. For background:

I believe Walter Schiedel questioned the geographical thesis. The Mediterranean was very possibly more conducive to integration than pre-Sui China, where all rivers ran west-east and there was no way to properly integrate the Yangzi and Yellow river basins (no Grand Canal, and maritime trade was poorly developed in Han China). And, of course, the Ottoman example shows that it certainly isn't impossible for an Early Modern state to attain control over a full half of the Mediterranean, while the repeated recurrence of the North-South divide in pre-Mongol Chinese history (between 184 and 1271, Beijing and Nanjing were ruled by the same empire for less than 350 years!) shows potential for two Chinas. Medieval Muslims thought North and South China were two different nations.
If North Africa and the Levant were the same religion as southern Europe, as they were in Late Roman era, I wonder if it would actually be more likely to see an at least partial Roman reunification than to not see one at all. Particularly with the Ottomans reuniting the Islamic parts of the former Roman Empire IOTL.
Yes, I'm inclined to think that Islam was what made Mediterranean disunity permanent. More specifically, the Muslim conquest of Persia and the resulting creation of a new Islamic civilization. As Robert Hoyland points out, if the Arabs had conquered only the Levant, Egypt, and North Africa, they would probably have Romanized like the Germanic conquerors.

Edit: Or one could imagine that had the Arabs failed at Qadisiyyah but conquered Constantinople, the new Roman Empire would be a Muslim Arab one. Which would have certain parallels in the conquest dynasties of Chinese history.
An interesting, but probably implausible, potential TL could be the Arabs failing to take Persia but absolutely steamrolling the Byzantines, Visigoths, Franks, and Lombards, uniting the whole Mediterranean basin and in the process becoming completely outnumbered by their new subjects, the only unifying factors of this empire being Romanization and Islam.

Due to the logistical factors of Tours and the Sieges of Constantinople, and the political structure of the actual Umayad Caliphate, I suppose it's "Alexander goes West"-tier plausibility, though.

Then again, without Arab settlement in Mesopotamia, Arab settlement in Tunisia and Anatolia could provide two new powerbases.
What if:
  1. The Caliphate failed to conquer Persia or Mesopotamia; focusing the energies of Islamic armies and Arab settlement to the extant or former areas of the Roman Empire.
  2. The Caliphate conquered all of the Maghreb in its first campaign there. No Byzantine-Umayyad back-and-forth until the the Arabs solidify their control. It all happens in one fell swoop, conserving resources.
  3. As difficult as it may be to achieve, Constantinople falls in 674-678, leading to Byzantine anarchy.
  4. Iberia is conquered on schedule, or before, if possible.
  5. With more resources focused on the West, and a now Constantinople-focused momentum, the Arabs launch punitive campaigns against the Avars and/or Bulgars, establishing a loose control and defensive line in the Balkans.
  6. Expanding Arab naval power in the Mediterranean allows the destruction of Lombard trade, and an expedition into Sicily--possibly a continuation of the war against the Romans--allows the Umayyads to subsume southern Italy.
  7. Finally, the Umayyads push north to conquer the rest of Italy as well as connecting their territory in al-Andalus to Italy to the Balkans, completing the conquest of the Mediterranean Basin.
  8. (Optionally) the Umayyads could also push to the Loire, humbling the Franks.
Although likely implausible, it's an interesting idea to ponder, as these ultimate military successes would establish the Umayyad Caliphate as a geopolitical successor, or a "new dynasty" of the Roman Empire in the style of some Chinese dynasties.

The Arab centrism of the Umayyad Caliphate may make this difficult, however Muhammad bin Qasim who conquered Sindh for the Caliphate, did incorporate Hindus and Buddhists into his administration. In areas like Lombardy and the highly populated Asia Minor something similar may be necessary. This practice could spread outward out of necessity.

Without Arab settlement in Mesopotamia, Arab settlement in Tunisia and Anatolia could also provide two new powerbases.

It would go against Umayyad nature to Romanize... But with even more stresses on the Umayyads, perhaps a sort of Abbasid Revolution (this time originating from the Greeks, perhaps?) would realign the ideology of the empire and use the two unifying factors of this ATL empire, Romanization and Islam, to construct a new legitimacy.

What sort of state would form if the Caliphate practically usurped and then reunited the Roman Empire in an even faster series of lightning campaigns?

Also, it could be interesting to explore following "foreign dynasties of the Roman Empire" that unite the empire. The Franks would remain with some of their advantages, perhaps 2-3 centuries afterward, they end up conquering and reuniting the Roman Empire? But ironically, by that point, it may require any ATL Charlemagne to convert to Islam.