I'm not part of your line of Alexanders, but perhaps I can shed some light on your "why Ky." question.
The Comm. of Va. laid claim to Ky. and much of the land west to the Mississippi River. About 1800, Va. and other "claiming" states were induced to give up their claims. Kentucky, Ohio and many other eventual states became territories of the US. Some of the land in these territories was "gifted" by the US to veterans of the Rev. War or their descendents. Even the land not gifted was very cheap compared to that in the eastern states, so settlers looking for large (or small) tracts of fertile land were drawn from Va., SC, NC .
My line of Alexanders was well established in Va., but my gg-granddad and his new wife left for Bracken Cty, Ky. in about 1800.