Ruben - I think you're a genius. I pointed my new 7.6.2 install to the old 7.1.1 sql file and the system came up with what appears to be all users and posts intact. Of course I have to go back through the CP and make some updates, but that is minor. So I think I'm in business. I do have to do more checking to be sure everything is working. Thank you so much for the suggestion.
Were there any sql file updates between 7.1.1 and 7.6.2 that might come back to bite me? If so, is there a script to do the update available?