Yes, "Studies of [the variations in] human DNA from populations around the world suggests a common African ancestry living some 200,000 years ago."
So if you give the studies credence, you are implicitly accepting 200,000 years, not 6,000 years, as the date of the bottleneck.
Of course, if you accept these studies' validity, you must also accept, for exactly the same reason, that humans and chimps split off about 6 million years ago.
Also, if you accept these studies, it's clear that the bottleneck occurred in Africa -- not in the Holy Land.
Finally, there are non-miraculous, non-flood explanations for the bottleneck. Namely, that the modern humans that came out of Africa outcompeted the Neanderthals.