It is nice to see your post, as the Truman posts at genealogical websites seem to be few and far between. About your Alexander, I believe it is he that George Washington is talking about in his letters, who was killed by the Indians. Also, he is mentioned in the Congressional records as they were awarding funds to his children, and so forth. I know of these letters and Congressional records from the Library of Congress website. If you do not know of them, I am sure you can find them.
If you are not in touch with Beth, a dedicated Truman researcher who posts to this website, you may want to contact her. I believe she is descended from a Maryland line, though I do not know if it is yours. I am interested in the information you have on Alexander's descendants, so that I can see if there is a link to my lines.