Has anyone out there tried installing an internal hub on a Schwinn Phantom (1956 Green Phathom)..... or heard of anyone doing so? I'm restoring one and can't resist the urge to hotrod it just a little.

You can do it. No reason why a Shimano Nexus or Sturmey Archer hub wouldn't fit. But you'll probably want to upgrade to drum brakes for more reliable stopping power.