An Islam-screw or Arab-screw might achieve this. Greek was still a growing language before the Arab migrations, and if the invasions that allowed arab tribes to spread, bringing with them Arabic and Islam, are aborted it could allow a Byzantine resurgance. If Islam and Arabic never make it the Egypt, there will still be Greeks, and Coptic will either continue to exist while being more influenced by Greek, or be replaced Greek like it was Arabic otl.
Honestly, even though it's not what the challenge is, I really like the idea of multiple Greek-descended languages existing in the old Byzantine empire. Would the languages look like the Romance languages, as in they have a large amount of similarities but are too divergent to be considered dialects, or would the relarionship look more like the Swedish-Danish-Norwegian continuum, or other mutually understandable languages like Russian and Ukrainian or Serbian and Croatian? I would imagine that it could look more like otl Arabic, where the same language is used from Morocco to Iraq, but with staunch differences, but this seems most likely with a Byzantine-wank.
The POD is so far back, you could really work toward multiple possibilities, but I'd have to imagine in the most realistic scenario the Byzantine empire falls eventually into multiple successor kingdoms, which could codify the language, either to enhance linguistical-cultural ties by keeping the inevitable dialects as close as possible, or make as many arbitrary differences to separate their identity. Or, maybe a mix of the two across history.
And as for the Turks, I could be wrong but it seems likely to me that without Islam, the Turks would either be assimilated, or when they do found a new nation/empire it wouldn't so much be "new". If the Turks still conquer modern day Iraq, perhaps they become Nestorian instead of sunni, and move on to create a Nestorian Turkish dynasty of Rūm on the ashes of the Byzantine core. If I remember correctly, DNA studies of the Turkish populace show a remarkably high genetic component of people's native to Anatolia compared to a relatively small Asian component, so without Islam to differentiate identity, do the Turks bother trying to keep their old language, or just use Greek which is already widespread for trade, military, administration, etc? I'm sure there is dispute on that, but I'm interested on opinions, and personally I think it would be more like the Visigoths in Spain; different variety of Christian, different language, and they assimilate for convenience as rulers. I imagine the comparison wouldn't end there either, as I could see the Turks being disliked by the Orthodox Greek majority, the how the Copts would feel about the whole thing eludes me. Would Copts prefer Orthodox or Nestorian Constantinople?