Ugg. Leave it to me to over-complicate things! I tried a bajillion combinations of settings, and eventually started widdling down to something simple.
First, here is the customBinding equivalent of wsHttpBinding, out of the box:
http://webservices20.blogspot.com/2009/04/wcf-custombinding-equivalent-to.html
From there, I started building up, and the config below ultimately did it. I have the ServiceContract attribute specify to sign-only. Then in config, the "Kerberos" mode takes care of Kerberos Token Profile, and the httpsTransport takes care of SSL! That did it! Maybe this might help someone else in the future:
<customBinding>
<binding name="KerberosTokenProfileSignAndSslBinding">
<security authenticationMode="Kerberos" />
<httpsTransport />
</binding>
<customBinding>
EDIT: I ended up writing a blog post about the details, in case anyone reading this needs them - http://robertseder.spaces.live.com/blog/cns!587F478B9240C01E!773.entry