[exim] MX for Multiple Domains using Exim4 as smarthost

I have an Exchange server that I use to host 3 domains for our
organization. (I wonder how many users stopped reading there.)
I have set up a Debian box with Exim to act as a smarthost. (Please do not
send me to the Debian users group. This is not a question about the Debian
setup.)

I can successfully send mail out of our network, and I can send email from
one domain to another on the inside of my network. I am trying to set up
the MX records/reverse DNS records with our ISP/Domain registrar.

I am unsure of how to proceed because my smarthost is the server that
receives the email on the edge of my network for all of our domains.

My Exchange server looks like gcmmail01.domain1.com, gcmmail01.domain2.com,
and gcmmail01.domain3.com when I send the mail. I have set up host records
with these names for the external IP for each. I have set up a reverse dns
record for each also.

I can not connect to my server from the outside. At this point, I don't
know if it is the settings on my edge router, or some problem with the Helo
because of the way I set up the MX records.

To be honest, I think it might be a little of both.

Is it OK that the MX record points to a server that has a different FQDN?
The server is not named gcmmail01.domain1.com, or gcmmail01.domain2.com or
gcmmail01.domain3.com? The records point to IPs that NAT to
MailGateway.domain1.com (the smarthost).

I have set up servers to point to a smarthost, but this is the first
smarthost I have configured.