Is it possible to connect two Tri-color LEDs and control them separately?
Yes but you will use another 3 pins.
Which of course is exactly what I am trying to avoid. It looks like it may be possible to Charlieplex
the Tri-color LEDs?
The problem is you don’t have 3 separate LEDs. They all share a common anode. So the normal Charlieplexing scheme won’t work.