I thought that it was going to be the classic young officer makes good on the frontier story. The Ludlow type situation and unrest angle is interesting.

You might want to check out, if you haven't already, The Iron Heel by Jack London.

David Drake writes some novels along those lines, though he tends to set his in the future or Roman times rather than an alternate time line. He's the guy who wrote Hammer's Slammers. Worth checking out.

Do they have Babbage machines?

A simple point of departure for such a timeline is to have had Fergusson actually take the shot and kill George Washington. Fit it into a prologue and the reader gets a flare for the differences. That or cover art with Red Coats on horses fighting Apaches or some such.

It helps to have a woman involved. Easy source of conflict. Gives the young officer and the everyman type something to compete over. If you like period Jack London pieces you can make her a socialist agitator or anarchist or some such. For extra challenge she could be ruthless and simply using them both.