[Exim] Non existant host (HOST_NOT_FOUND)

I have some machines in domain.com, I have configured exim to forward all
@domain.com or @"host".domain.com to the main internal mail server. (Although
some users are local pop3 accounts or internet, working.)

My new requirement is for all mail for @list.domain.com
should be sent to an internet mail server. This obviously breaks my
*domain.com `being local` rule.

I have created a router entry :-

list_domain_smtp:
driver = domainlist
route_list = "list.domain.com internet.com bydns"
transport = list_domain_smtp

with a transport :-

list_domain_smtp:
driver = smtp

This rule works when sending mail to @list.domain.com from the exim server (the
only machine with internet access (on port 25)

mail_server$ /usr/exim/bin/exim -bt user@???
user@???
  deliver to luser@???
  router = list_domain_smtp, transport = list_domain_smtp
  host internet.com        [xxx.xxx.xxx.xxx]  MX=100

But sending from any client barfs. Obviously, as list.domain.com doesn't
actually exist it is not DNS registered.

mail_client$ exim -bt user@???
/usr/exim/bin/exim -bt user@???
user@??? is undeliverable:
unrouteable mail domain "list.domain.com"

How can I get around this ???

As a side, most mail_clients are running sendmail.. :-(

Any help much appreciated.

Andy Holmesbegin:vcard
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version:2.1
email;internet:andy@???
title:UNIX Consultant
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fn:Andrew Holmes
end:vcard