To anybody else having this problem:
There is a bug 7129 in bugzilla that is apparently the same as this bug. I don't really see the connection, but I'm not a coder.
http://bugzilla.zimbra.com/show_bug.cgi?id=7129
I guess I just don't understand how something as basic as renaming a user can cause these problems. I wonder if there is a way to get the calendar working for my users if I rename the account to the old name and then share the calendar with the new name or something.
If Importing/exporting with Outlook would work I would even do this.
The worst thing about this is that I look like an idiot when I have to go tell this user that he's got to go through his whole calendar and remake all of his appointments again, after he just had to do so because of the switch to Zimbra in the first place.