This is due to permissions issues:

Jun  4 04:16:51 jrmu smtpd[71633]: dkimsign: Can't open key file (/etc/mail/dkim/private.key): Permission denied
Jun  4 04:16:51 jrmu smtpd[50276]: warn: lost processor: dkimsign exited abnormally
Jun  3 01:30:08 jrmu smtpd[63168]: 366fb2a5ce9a0764 smtp envelope evpid=2fee16ca81516ba5 from=<> to=<>
Jun  3 01:30:08 jrmu smtpd[63168]: 366fb2a7e3bb9d4b mda delivery evpid=2fee16ca81516ba5 from=<> to=<> rcpt=<> user=jrmu delay=0s result=Ok stat=Delivered

Note: I cleared up the permission error on nastycode by adding _dkimsign and _smtpd to the _dovecot group, and then add group read permission to that private key. I'm not sure whether this is advisable, from a security standpoint, but it did mean that smtpd came up properly.