Well, I looked through the solutions that the yahoo search above came up with - to no avail. I did end up finding something that helped.
[SOLVED] SOLVED: Zimbra 6.0.1 stop working if SSL certificate is expired
in combination with
Recreating a Self-Signed SSL Certificate in ZCS 4.5 & 5.0 - Zimbra :: Wiki
The step listed by Eaperezh initially failed but the wiki was far too involved for what I was wanting to do. So, comparing the two solutions revealed what to do. Doing the steps listed by Eaperezh in the order of 1, 4, 2, 3, then doing the LDAP step that he listed at the bottom solved my cert issue.
I do have one thought that I'll worry about next year. Eaperezh says to create the cert with the -days 365 switch but the wiki doesn't mention setting a day count. If I had left the -days 365 off, would it have created a cert that would have never expired?
Mike