I have contacted clara.net, and they have pointed out that the emails are not going through the correct server -- although ListMailPro, which you set up for me, specifies "relay.clara.net" the emails are actually being posted through clara.net's main serever, which has strict limits on email volume.
(The SMTP logs show that the emails are going through xxxx.clara.net, NOT through yyyy.clara.net)
It seems that the ListMail SMTP sever configuration is not correctly reflected in the actual email broadcast.
Can you help please?