I would try two things, modify the rsyslog.conf file in the GUI again, then save changes (to apply it again)
or check to see if the Cluster is in Sync (configuration > cluster, then check the configuration timestamps to make sure the nodes are in sync)
Fixed. To be clear, for future posterity, what I ended up doing was this:
I went to the settings for "File System Logging" (actually, by way of the logging rule) suspected of being the culprit and I toggled a couple of check boxes (log buffering and header writing), and hit save changes. I immediately re-toggled those settings and hit save changes again.
A tail -f messages shows:
Jun 4 03:37:01 SFC1A rsyslogd: [origin software="rsyslogd" swVersion="4.6.2" x-pid="11576" x-info="http:/ /www.rsyslog.com"] (re)start
But, no more access logs, thankfully.
(And, it's under configuration > appliances that I find the time stamps.)
Thanks for the tip.