I've discovered something which appears to be reproducible across a clean installation... I suspect it's a bug in monit actually, but I'm not entirely sure.
Initially I thought I borked my configuration badly, as monit was unable to establish a connection to 127.0.0.1:443 which causes the daemon to restart nginx constantly, flooding the syslog.
So I did a clean installation, reproduced my configuration by hand and... in fact, I have discovered that creating a 512b length RSA key for your OMV certificate will cause monit to throw this error no matter what, regardless of whether or not there's any actual problems establishing a connection to lo at that port. Creating even a 1024b key ameliorates the problem.
I know I had read that TLS is pretty pointless for LAN-only installations, but I don't really trust any device whether it's from the world wide web or my LAN.