Separately, I think it's great if you can have all of your employees involved in the support and outreach process, but that's a cultural thing and thus a bit harder than changing a mail header.
"Who should I contact to solve my problem?"
The ideal experience in my opinion is a single contact point, with the authority and knowledge to solve every issue you have.
That's of course unrealistic, but I want to find a way to approximate that. The closest thing I've heard is Alla Klein:
http://code.dblock.org/alla-klein-a-fake-person-in-charge-of...
But note that this is not zero cost. The time your support staff spends deleting out of office replies and spam is time they aren't helping real people.
Reading every feedback email from every real user teaches you how to create better products. If you make it clear users can provide feedback, there's an opportunity from them.
I ask every single real person who leaves my service why they left, which translates to about 12 emails from me per week. Most of the time, the feedback isn't actionable, but 2-3 of every 50 emails translate to something I can use to make my product better.