v> The event log says something like:
v> "Message delivery to the remote domain 'mydomain.com' failed for the
v> following reason: The connection was dropped by the remote host."

.... which isn't a DNS problem at all, let alone BIND-related.

v> But I think what's happening is mail addressed to "mydomain.com" is
v> never being sent to the mailserver...like the MX record's being
v> ignored and it's trying to send mail back to itself.

There's no need to flounder around and hypothesise what is happening.
The error message *says* *exactly* what is happening. The SMTP Relay
client at your end made a connection to the SMTP Relay server that it
had looked up, which latter then dropped the connection from its end.

Like so many people with "I'm having mail problems, how can I fix my DNS
service?" questions, you aren't _reading the actual error messages_ from
your mail system.