One thing to consider here is that blacklisting is usually based on IP addresses. Separate headers won't help much there. The reason for this is that (a) it's simple and (b) many spam sending servers have been compromised and taken over by an attacker, using custom mail sending software, so headers don't matter anymore.
Different headers might still have their merit though, as spamfilters will check those. It just won't help if your server's IP gets blacklisted.
I guess rolling out DKIM might help here, it would give you artificial separation of domains using different domain keys for each. There are some good tutorials on the net on how to set it up with OpenDKIM.
A better solution, used by big mail providers like GMX, is to send mail from a separate IP if it looks like its spam. The setup for this is a little complicated, as it requires you to scan outgoing mail with spamassassin (or something similar) and to route mail depending on the respective spam value. Not an easy task. Marking spam as such, without sending it through a separate IP, might enough to convince the other side that you try to prevent spam send from your server, but this really depends on their spam filter.
The way your server identifies itself during an SMTP conversation is through the HELO command. The smtp_helo_name parameters specifies the name used there. One could try to setup a transport mechanism to use a different name for each sender domain. I'm honestly mot sure how difficult that would be.
If you are still set on changing headers: the header_checks tables not only allow to remove headers, but also to alter them via regular expressions.
Use the REPLACE command to do so. Example:
/^(Message-ID:.*)@your-domain.example(.*)/ REPLACE ${1}@other-domain.example${2}
I'd advise against it, though. It provides to little gain for the effort of finding and setting up the right rules.
