I think that you miss the point. The timing will be affected by the start point.
If your quote accurately reflects Sanford's views, he says:
...the population plummets essentially to zero... in just 300 generations.
Obviously the human population is not "essentially zero", so humans must have been around for less than 300 generations, right ?
That would fit quite happily with a timescale of 6000 years, but not with an Old Earth timescale (which cannot be much less than 200,000 years).