Well, as I said, it is not perfect, but it does what I need.
When I change the sender in the way I described, the receiver of the email sees the changed email address as the sender, and replies are send to that address as well.
However, looking at all the headers of the mail, the real sender can still be determined, as it is stored in "Return-path" and "Sender". But for the average receiver that does not show (at least not with the email clients I checked).
You wrote that this request has been turned down before, but I can't find it. Do you have a link to it?
PS: Thanks for the advice with using several location documents. I have sent out hundreds of different email addresses, so that's a little bit hard to do. Actually, I was using one location document that I edited accordingly when needed. The lack of support for multiple sender addresses is the only reason for me why I look at other email clients from time to time (but obviously I haven't found anything to my liking as yet).