but if said Emperor secures himself in power, you might see an adoption by the Orthodox of some Islamic ideas - or, conversely, a Greek form of Islam which maintains many Orthodox notions (the divinity of Christ, for instance).
Hellenised Islam wouldn’t maintain the divinity of Christ- that’s such a big change that you simply can’t call it Islam. Allah is without associates or equals- unless you take the mention in the Quran of Mary being impregnated by when spirit was blown into her through Gabriel, and equate that spirit with the the spirit of Allah that was breathed into Adam in the Quran to get an Islam where the Holy Spirit is a much more important concept from the beginning.
An interesting point to mention here is the view of Nurbakshi sufis which formed part of imperial Mughal ideology- the divine light which took shape in a human mother without a fathers loins, assumes holy bodily wrappings in many manifestations including Jesus, Alanquas son and in the present day the emperor Akbar. Safavid imperial ideology under Shah Ismail too held that he was the present embodiment of Jesus, Ali, the twelve imams etc
For the Nurbakshis it wasn’t a question of reincarnation, but one of projection, where a complete soul pours into a perfect being and he becomes the locus of its manifestation- this could happen between two people both alive at the same time but nurbaksh used it to explain how he became Jesus.
“in Irbil in the year 827 [1423–1424], that one day people gathered together to wait for Jesus to descend from the sky. He saw that he descended in the form of light rather than body, and flowed toward me [i.e., Nurbakhsh] and held me. The same night I saw that I was present in the sky and in a human body on earth in the same instant.”
These examples are from a radically different Islamic culture than existed in its early days, after centuries of evolution and exposure to Buddhist, tengrist ideas- but the point I’m making is that the claim that Jesus was a being of light who united with ahuman body seem pretty apollinarian, and could be taken as a revival of that stance- if the early Muslims decide it’s acceptable to them in the way it became obvious to Muslims of the 15th century. Alternatively the whole- they thought they killed Jesus because that’s how it was made to appear to them could be a neo-docetism thing of and he was never really flesh anyway, just divine light made to look like flesh.
Hellenised Islam might take the New Testament to have real authoritative worth on how to live your life well, in all the sections where it isn’t contradicted by the Quran or Hadith.
After all the most widely accepted Islamic position on the New Testament otl is that
“The Injil spoken of by the Qur'an is not the New Testament. It is not the four Gospels now received as canonical. It is the single Gospel which, Islam teaches, was revealed to Jesus, and which he taught. Fragments of it survive in the received canonical Gospels and in some others, of which traces survive (e.g., the Gospel of Childhood or the Nativity, the Gospel of St. Barnabas, etc.)”
For hellenised Islam, it just becomes obvious that even if the injil of Jesus was misinterpreted, large portions of the New Testament which don’t contradict the Quran or Hadith are a source of law and theology, at least equal to Hadith. This includes much of the picture of the personality of Jesus, who chased the moneylenders from the temple or who taught the sermon on the mount. From that, Jesus for hellenised Muslims can take on the position of a culture hero like Ali was otl- not divine, but with people having such a strong emotional connection to him that they self flagellate in his memory.