The "vxdmset" mentioned was part of vasm originally, but the most recent vasm-legacy doesn't have it; it's unavailable unless one grabs the old source. Setting display manager manually by editing rc.X is a valid method. Why not list all of the display managers up front, comment each out, then uncomment the one used. A cheap way of documenting the possibly available display managers.
#DISPLAY_MANAGER=KDM
#DISPLAY_MANAGER=GDM
and so on.
The entries as you have them are fine, though it would be more consistent to add slim to the "for" list too, so it can be tested when DISPLAY_MANAGER isn't set, like the rest are.
Because of the chance of breaking someone's configured, working system (and a few other reasons), I'm guessing that an offer of a new official rc.X for 7.2 may not be accepted. It's easy enough for interested users to customize on their own while 7.2 is the current version.
The problem is in slim's configuration. If you installed slim from the command line, you were shown a note to check out /etc/slim.conf.new and /etc/logrotate.d/slim.new. If you haven't, rename each of those without the .new extension.
Now look at /etc/slim.conf:
login_cmd exec /bin/bash -login ~/.xinitrc %session
That's only going to work when a user has an .xinitrc that looks very similar to the sample provided with the Slim source code. (It would be nice to have that copied to /usr/doc/slim-*/, but I'm not taking the time to do that.) Comment out that login_cmd line in slim.conf. There must be better ways to do this, but here's a working line so you can get on with what you're doing:
login_cmd exec /bin/bash -login -c ". ~/.xinitrc || . /etc/X11/xinit/xinitrc"
A Bash shell is started with a fresh environment just as in a terminal login, except that what follows "-c" is executed: That shell tries to source a user's .xinitrc; should that fail -- usually because the user doesn't have one --, then /etc/X11/xinit/xinitrc is sourced. That's usually a link to the system's default desktop session, as distinguished from the default session that's just an xterm. A VL installation has that linking done by default.
Gdm, and I think Kdm, use a different method. The user's preferred session type is given in ~/.dmrc. I once chased down exactly how things end up there, but have forgotten. Can anyone remind me? Anyway, whatever Session= is pointing to, the desktop file /usr/share/xsessions/<Session>.desktop is read and its Exec= setting is executed, with "default" being a special case.
A lot of different ways to go here, but the edit above to slim.conf will get you something working. The flash you mentioned elsewhere that GDM has isn't present for Slim. I resized my desktop wallpaper to fit my screen so that it wouldn't have to be resized on the fly. Icewmvmods is my DE. Because spacefm has a flash of its own and doesn't handle background transparency on startup, I disabled spacefm control of the desktop in the IceWM startup file, then set IceWM preferences to have icewmbg handle the background. Then I set both Slim and icewmbg to use the background made from the wallpaper above. As far as can be seen, all that happens after login is that the word "Login:" and the text-typing box disappear, leaving me in my desktop and looking at the same wallpaper, with no flash at all.
Nice find. I think we'd all forgotten about Slim.