Next step was to get libchamplain working so that the location data can be shown on a map. That turned out to be pretty easy. I found the easiest way was to do a
git clone of their current repository. Doing that also meant that I could look at some of the example code, especially the python bindings they have with that library.
git clone git://git.gnome.org/libchamplain ./autogen.sh ./configure make sudo make install
launcher-gtk.py particularly helpful in understanding how the map drawing works.
If you prefer to just install the binaries, then this should do the trick:
sudo yum install libchamplain-devel libchamplain-gtk-devel libchamplain-demos
With both GeoClue2 and libchamplain installed, I now had enough information to get started on my mini-project to get my current (IP-based) location plotted. The code for this can be found here.