OK. Looks like we found it. Taking a clue from a /etc/inittab, we checked out a file called /etc/sysconfig/desktop. This file contains a single line:
:Changing that to "KDE" changes the login manager. In our case, we get the typical blue RedHat 7.1 background with a somewhat small version of the KDE login manager.
X looks a little weird as it comes up so I hope there are no side-effects to making the change. Not that I can think of any reason why there would be.
Thanks, all, for some great advice!!!