Hi Chuck, first of all, you didn’t re-scale your Object, but Applied the Scale. (The Scale has changed, but the Dimensions are still the same!)
So instead of CTRL+A > Apply Scale, just set the Scale to (1, 1, 1) manually (in the Properties Panel).
As to the second question: if I understand correctly what you are trying to do: NO!
The only thing you could ‘transfer is the Settings of the Particle System (amount of hairs, Length, etc…), but not where the hairs should be (the hairs are connected to the Faces of the cap, that are numbered internally and the other modell has a different Face count and different numbering, so that could never work) and you would also lose all the grooming (Particle Edit Data).
