... with a POD as early as 1071, how would the Eastern Roman Empire and the Ottoman Empire survive to present, preferably with Anatolia and the Balkans split between the two, and with both powers relatively balanced?
Impossible. A Turkish state coexisting with the ERE is concievable, but probably not the Ottomans, who only really came into the picture once the Empire was in its final death cycle.
Possibly, yes.Oh, I see. So if we butterfly away the Ottomans, but we leave the Seljuks in, we can have both states coexisting?
I'm also thinking that it could stifle the rise of Austria; didn't Austria essentially define itself as "Europe's vanguard against the Ottomans"?
You have more possibilities if you consider Seljukids Turks instead of Othman ones
Except by the time the Ottomans come on the scene in a significant way, the Byzantine empire is already living on borrowed time: they've lost the entirety of Asia Minor, everyone is kicking their ass in the balkans, and two or three rival claimant princes still exist, while Constantinople is in such a state of decline that it had already barely 100.000 inhabitants by that point. They barely have an army at all and the situation of the lands is basically hardly good enough to do much of a levy.
You'd need quite a huge POD to even have Byzantium live, let alone survive in a way where both them and the ottos would be ready to coexist without the ottoman sultan pursuing the crown.