Here's a reference and a quote from it indicating the accuracy of the cheetah bottleneck estimate,
"If the mutation rate of the feline FCZ8
family is comparable to the above four rates, the time
required to produce the cheetah's level of variation would be
estimated respectively at 3,529, 6,000, 11,765, and 12,766
In short, it could have been 4500 years ago. What's next?
So the Data says it would have taken longer. But you assert that it would not have taken as long.
And a cheetah is one of your best case examples.