Finally found out that I was using the wrong syntax for the set-log-level command. (Why did it say 'access denied' instead of 'bad syntax???) Changing the log level all the way to emerg still had no effect. And in my logs during reboot, I'm seeing this message:
systemd[1]: [/etc/systemd/system.conf:11] Invalid log level'warn': Operation not permitted
even though /etc/systemd/system.conf doesn't contain LogLevel=warn (anymore) - it has LogLevel=emerg!

Why isn't systemd reading the CURRENT /etc/systemd/system.conf file? Why does the command line setting seem to have no effect? Is systemd this hopelessly broken?