My wife and I too would like to know the ancestry of Joseph Lowery Alexander (her multi-great grandfather); however, from my research, I am fairly confident his father is not John McKnitt Alexander, although I would be happy if the father could be shown to be JMA or anyone else.
A more-likely candidate for JLA's father is in the line of Elizabeth Alexander, who married Samuel Tate, Jr, in Augusta or Rockbridge County, VA, February 1785. Her father's name was, by tradition but possibly not from record made at the time, Joseph Alexander also. This could have been a case of brother and sister marrying sister and brother.
A simple DNA test will settle the issue of whether the father is JMA since more than twenty men descended from JMA's grandfather or his grandfather's brothers have been tested in the Alexander DNA project. I'll make a deal with any male-line descendant of JLA. Take FTDNA's 37-marker YDNA test, and I'll pay for it if the results match JMA's line.