Just a note in case anyone else runs into this -
The box that the instructions told me was supposed to show my name was blank, and the formatting of the URL didn't actually contain my id but rather a random long number, and entering my user name or that number did not allow Launchbox to access my account.
I manually entered my user name into the blank box of the "Custom URL" line on the "Edit My Profile" page, and saved the changes, and after that Launchbox was able to access my account.