>Religious stories about the Buddha were readily and literally coopted into Christian lore by early Church writers.
That's just another assertion of "They copied it!" Where is the evidence that this is so beyond an inference that they were copied?
>Unless you presume the Buddhist stories were themselves historically accurate - which would start down a road of "both Buddhism and Christianity are true" - it's hard to imagine that these were coincidentally also stories about real figures.
Life is suffering, and the Messiah took all human suffering on himself? I'm not sure these are mutually exclusive.
We have records of versions of the story being repeated as it travelled from South Asia to the Mediterranean and the name slowly changing from bodhisattva -> bodisav -> Būdhasaf -> Iodasaph -> Ioasaph -> Josaphat