Andy!  You asked about playing a MIDI instrument, live, long distance.
I'm not sure about the Internet but I am told that Yamaha did (or does)
this in Japan with their pianos.

The way I understand that it works is that they use a Yamaha
Disklavier in a live televised broadcast of a piano performance.
Somehow they encode the MIDI out signal from the piano in the broadcast
video / audio.  In your home, you have a decoder on the video signal
connected to both your television and piano.

The net result of this is that you watch a live piano performance on
your television, turn the sound down on your TV, then hear (and see)
your own piano playing what your are watching on TV.

Sounds interesting!  (no pun intended!)

Gary Rasmussen
Mason, Ohio  (Cincinnati area)