The key difference between Turkey and Russia is that Russia doesn't want to join. Turkey put itself on that path from the foundation of the state. When you say they have histories that diverge from "much of Europe" which "much" did you have in mind? Greece? Bulgaria? Ireland? Spain? Every state in Europe has a history that diverges from much of Europe.

Turkey is already a member of NATO, so the "we've got your back" promises are effectively made already.

No-one has put forward a non-nefarious reason that didn't apply to other states who have already joined, which is the test to my mind.