Is this a failure of your MTA or the mailing list software?

I'm not 100% sure.

Can you send mail from this box otherwise?

Yes, I am 100% sure that's possible. This box has exim installed on it, and it allows me to forward all my emails I send from home through it, since most domains believe that my home IP address is "dynamic" (though I've had the same IP for 10 years now.)

Seems daft to fart about with the mailing list software if it's not that that's broken.

I concur.