How to make Anatolian languages survive?

As the title says. How can we make the anatolian languages (or at least one of them (which?)) of the indo-european family survive until today?
What would be the most plausible way to make that possible? Where do we set the POD? Which butterfly effects would be there for sure? And how would such a scenario effect the rest of the history?
 
Avoid Alexander or any form of Greek conquest.
Basically this.
But, for later PODs, well, Caria and especially Lycia are probably the better placed holdouts. Some form of local Anatolian vernacular likely survived there at least in the countryside to Late Antiquity, have a local written standard be developed then and create some political reason for the ERE to cultivate that tradition instead of opposing it (it would likely have to be something about religion, such as a local evangelizer writing down stuff in the local language that comes to be regarded as authoritative/significant enough). Late Antiquity saw the emergence of such local Christian written tradition within the Estern Roman Empire and around its periphery (East and West Syriac, Armenian, Coptic, Gothic, Old Church Slavonic, Palestinian Christian Aramaic, Georgian, Ge'ez, Old Nubian, perhaps Old Arabic) so if a distinctive non- Greek area "identity" in Southwest Anatolia emerges, it may happen. A problem is the comparative lack of major prestigious urban centers in the region.
 
An Imperial Roman-era conquest of Anatolia by a Persian dynasty would be a late PoD that might accomplish this—have the Parthians or Sassanids or whoever support the non-Greek groups as an alternative to Greco-Roman cultural unity.
 
An Imperial Roman-era conquest of Anatolia by a Persian dynasty would be a late PoD that might accomplish this—have the Parthians or Sassanids or whoever support the non-Greek groups as an alternative to Greco-Roman cultural unity.

Keeping the region a borderland between Persia and the Romans is pretty essential. Maybe have large groups of the Isaurians (among the last Anatolian speakers) convert to some heretical faith, and they end up writing down a lot of their version of the Bible and some extra bits. They thus become an ethnolinguistic group, and hopefully maintain their existence no matter the future of the region.
 
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