I have looked online and cannot find reputable sources to discredit the findings of my grandfather who visited his home "The Hermitage" in Nashville, Tennessee. Wikipedia and many others show him at 6'1" tall, but my grandfather claims the manniquins at the museum that held his clothes are no taller than 5'7". Is there any reliable answer to this question?
I cannot comment on Andrew Jackson's original height. However I think the answer to this might lie in the nature of the artifact instead of Andrew Jackson's height.
It is quite possible for textiles to have shrunk over time in museum collections. The abrupt changes in relative humidity that would have been uncontrolled for most of their storage is one of the causes.
Obviously I cannot say this for certain, as I have not worked with those clothes, but it would explain why the mannequins would be smaller than Andrew Jackson's original frame.
If you are really curious, I would encourage you to contact the curators or collection manager at that museum. I'm sure they would be more than happy to answer the question.
Good question!!