Fully-qualified name & Kerberos

I use Kerberos authentication for my Apache server that hosts my CGI apps. The URL's use the unqualified hostname (e.g. http://myHost/<http://my_host/>).

I'm now trying to set up HTTPS. I already have an SSL cert, but the tricky part is that the cert is for myHost.domainName.com (I didn't do it, and I didn't have any say in the matter). If I try https://myHost/<https://my_host/>, it gives me a cert error, due to the name mismatch. If I try https://myHost.domainName.com<https://my_host.domain_name.com>, FF gives "Authentication Required", while Chrome & IE prompt for a login.

I tried the fully-qualified name in iNav, and Kerberos worked perfectly.

Any thoughts?