[exim] Using alternate SMTP server for certain domains.

Excite.com bounces any emails I send to a member, because the IP of my
SMTP server is blacklisted (by them, not any large BLs). I contacted
them about it, and got a bunch of runaround and no changes. I am not a
spammer, and the SMTP server will only relay for localhost.

Anyways, through my DNS provider, I have access to an SMTP server which
requires a login. I tried sending an email to an Excite account that I
made through that SMTP server, and it passed just fine.

What I want to do is setup Exim to take an incoming message destined for
Excite.com and have it use the SMTP server from the DNS provider to get
the job done. Ideally, I would have a text file with domains where this
operation would be necessary to deliver mail, as I am positive that
Excite.com is not the only organization that is this bad. I don't want
to tell all of my users to use the other SMTP server as it will just
cause confusion, and I would have to give out the one and only
uname/passwd combo that I am given for it.

I'm not sure how to approach this issue. I am familiar with Perl under
Exim, and know a bit about the config, but I would like to know how I
can make exim do this transparently to my users, in the most correct way
possible.

Thanks in advance for any help.