[Kevin Krause]

try adding redirectPort="<your SSL port>" in server.xml to the HTTP connector.

Interestingly enough, that's already there in the default Zimbra generated server.xml... here's a snippet:

    <!-- HTTPBEGIN -->
    <Connector port="80"
        enableLookups="false" redirectPort="443"
        maxThreads="100" minSpareThreads="100" maxSpareThreads="100"/>
<!-- HTTPEND -->

I have to admit that I have quite close to zero knowledge about Tomcat, otherwise I'd probably be able to figure out a solution on my own.