I would agree that manzikert was the fulcrum around which power transfered from Byzantium to the Ottomans. So it's from here that the (anything like plausible) discussion should start.
In many ways the Ottoman state replaced the Byzantine one. In fact, the Ottoman's considered themselves inheritors of the Byzantine state. I'm sure the first Sultans to live in Istanbul gave themselves the title of Basileus too.
Arguably this aspiration to Byzantine "inheritance" helped ensure a smoother transition to Ottoman rule in the Southern Balkans.
In a wider sense, I very much doubt the Ottomans and Byzantines could have co-existed for long, it strikes me as more of an either-or. Stuff that i've read points to the almost inexorable westward push for land of central asian Turkic people. The Ottomans at times harnessed these movements, but were not always in control of them -they certainly didn't instigate them.
I guess only if manzikert had been a resounding victory for the Byzantines would they have had the momentum to hold off, never mind and push back the movement of peoples looking for land.
Then of course you'd have to think about how Tamerlane would have reacted to Byzantium and its Christian empire. I'm guessing things would have been worse for a Christian ruler of Constantinople/Istanbul with land in Asia minor than and Islamic one. AFAIK it was Bayezid's rivalry with Tamerlane that ultimately lead to conflict and his eventual defeat. Tamerlane doesn't seem to have been bothered about absorbing the Ottoman state into his own empire, more about humiliating Bayezid.
What made the Ottoman Empire strong (when it was) was its effective rule and economic solvency, both of which were dependent on gifted rulers and sound policies. Was the ruling class of Byzantium up to that? I don't know enough about Byzantium to comment with any authority, but my perception of them is that they were perhaps too introspective and traditionalist to keep the initiative in changing times. Thats not a very great judgement and is certainly coloured by what actually happened, so maybe if manzikert had gone the Byzantine way, things would have been different?
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