Hi Lisa
Yes, that is what has been worrying me. It looks as though he deserted from the English army, and then possibly from the US army, so he might well have been covering his tracks and giving other names, not completing census forms, and so on. I had found the Alex A and Alex F people you looked for, but they are not him, assuming the information is correct. He never used a middle name in any of the records we can verify. He had six siblings, but only one of them had a middle name, so it is likely that he did not have one.
I guess a lot of people named Douglas emigrated to the US in the 19th century, so there will be a lot whose birthplaces were Scotland and Ireland. His was England, but he has siblings born in Belfast, Ireland, and Glasgow, Scotland. So, again, he might have given the wrong information so the British authorities could not find him.
I have had a look at various records on Family Search and Find My Past, with no success, and am at a bit of a loss. The nice librarian has asked to be kept posted! But I shall be embarrassed to say I have found nothing! My only hope is that some descendant of Alexander will try to look for his or her ancestry and find this discussion on RC! But that is not a pro-active strategy. But Alexander might have kept his history from his family as well. I have found that in my researches.
Lisa, you have worked very hard, and I am very grateful. They say even a negative result is something, so thank you for that. I have kept a record of what you have done so I will not repeat it. And the websites you have found look interesting too. If anyone has any inspirations, please post them!
Harlemswife