Exim seems to be sending the same message twice, according to the log, although there is a difference in capitalization of the local part of the address.

That is correct. The RFCs are explicit in stating that capitalization matters for local parts. For remote domains, Exim is not entitled to assume case independence of local parts. I know, it is utterly silly, and it causes a lot of grief, but that's what the rules say. Here is a quote from RFC 2821: ... a command verb, an argument value other than a mailbox local-part, and free form text MAY be encoded in upper case, lower case, or any mixture of upper and lower case with no impact on its meaning. This is NOT true of a mailbox local-part. The local-part of a mailbox MUST BE treated as case sensitive. Therefore, SMTP implementations MUST take care to preserve the case of mailbox local-parts. Mailbox domains are not case sensitive. In particular, for some hosts the user "smith" is different from the user "Smith". However, exploiting the case sensitivity of mailbox local-parts impedes interoperability and is discouraged.