Hi,
"I take this to mean that the domain without a prefix is set to go to the correct IP numbers (which in fact it does, because it shows my Site#1 from my mojoportal installation)"
If it is reaching your mojoportal installation using the blank domain (ie without www) then DNS is setup correctly and no additional IIS host headers are needed. At that point setting up the host name mapping in mojoPortal should take care of it if you want it to resolve to a different site than your default site.
DNS and IIS host records can only point to your installation they don't point to specific site ids. As long as it is pointing to your installation then it should work fine to assign the host name to a specific site within the installation using the host name mapping in site settings.
If it doesn't bring up the correct site after assigning the host name mapping in mojoPortal, try touching web.config to receycle the app. Make sure the host name is not mapped to more than one site and make sure it is mapped to the correct site in site settings. Any host name that points to your installation but has no host name mapping in mojoPortal will resolve to the first site.
Hope that helps,
Joe