Could one of those impacts been the Barringer crater in our southwest of about 50,000 years ago? Would that be the right amount of time to travel from the Ort Cloud? Or perhaps the cluster of impacts that took place in Argentina a little over 4,000 years ago that may have been the cause of the disastrous First Intermediate Period in Egypt described so eloquently by Ipuwer.
Ooh, tell me more about the Argentine impact cluster!
50,000 years would be more than enough time for a comet to travel from the purported Oort cloud. Long-period comets (like Kohoutek) have orbital periods in that ballpark.
My view is, the stuff that hits the Earth is mostly nearby, and that the periodicity of impacts is illusory — they happen when they happen, and the greatest threats are near enough for us to identify them and do something about them.