Finally able to return my attention to this problem.
alsa-store.service and alsa-restore.service are oneshot services with no
[Install] section. Therefore, they cannot be enabled and disabled using
systemctl. They do, however, appear to run as needed, probably as a
dependency when udev loads the modules for the sound device. I find that
the volumes are always saved at shutdown and restored at boot time, but
something in gdm or gnome-settings-daemon, or possibly even Pulse itself
is muting the volume, although it seems unlikely that Pulse is doing it,
because if I restore the master volume after gdm starts, either using
alsamixer or by explicitly running alsa-restore.service, logging into
GNOME once again mutes the master volume and sets it to 0. Apparently,
Google is not my friend this time, as I can find no information about
this problem, and I appear to be the only one experiencing it, and only
on this machine. Additionally, I resized the existing partition on this
machine's hard disk and installed Arch into the free space, just in case
something was behaving strangely because Arch was installed to a thumb
drive, but the problem persists. Any help with this unusual problem is
greatly appreciated.
~Kyle