I have two Elizabeth Bedingers --- or maybe they are the same one, intermarried between different lines. In fact, your posting drew my attention to this. The one I think you mean was born in 1755, daughter of Henry Bedinger (b. 1729, in Dorschel or Durstle, Alsace and d. 1772 in Shepardstown) and Magdalena von Schlegel (no further data). This Elizabeth is said to have married an Abel Morgan. If this is the same Abel Morgan, you aeem to have more data on him than do I. I do have his father as Richard ap Morgan, said to have been born in Wales.
I have another listing for an Elizabeth Morgan who is the daghter of an Abel Morgan and Elizabeth Bedinger, but I never noticed before and now think this Elizabeth is probably the daughter of the same Abel Morgan and Elizabeth Bedinger. This Elizabeth Morgan (b. August 27, 1784; d. May 28, 1852)married (May 05, 1807)my direct ancestor, Matthew James Ransoné (the final e was dropped in the next generation).
I also have an Abraham Morgan who is said to have married Anna-Maria Bedinger, daughter of the same Henry Bedinger.
I believe I have more Morgan information somewhere which I have not yet entered into organized material and the names William and Daniel Morgan are familiar and I beleive I have seen them listed as related.
I also have an Elizabeth Bedinger, although I have not yet figured out which of my Bedingers she is, who marrie(September 24, 1793) to John Thornton Washington, who was the grandson of George Washington's brother Samuel. I'll privately email you what I have on that line.
If you can help me fill in any of my blanks it would be greatly appreciated.