Lawrence (and all more generally),

At its last network update (3a today, the beginning of the 2-hour window mentioned above), without my changing any settings after having installed the 32-bit libraries "lib32-glibc" and "lib32-glib2", the machine in question successfully downloaded CEP2 WUs and their attendant project files [now listed in the 'apps' output of "boinccmd --get_state".

This suggests that WCG won't download the CEP2 (or any sub-project) files until it expects to do a CEP2 work unit (which makes total sense given the frequency, length, and prevalence of WCG sub-project inactivity), and that I would have resolved this issue sooner if I had edited the machine's WCG profile to only do work from CEP2.

Solution Summary [for Arch Linux (but probably all Linux more generally)]:
Fixed by installing

lib32-glibc

and

lib32-glib2

but it won't appear fixed until the machine is assigned a CEP2 work unit, which may be a while. You can force this to happen sooner by making CEP2 the only checked project in the machine's WCG device profile web settings.