Kenneth,

There is a schedule in which, over 5 days, every pair plays together exactly once. You can find that in the archive, search for golf 16. What I suggest is to use that schedule for the first 5 days with one assignment of players to symbols (i.e. george is player 1, Ed is player 2, ...), for the next 5 days with a different assignment of players to symbols (now Charlie is player 1 and Ken is player 2, ...) , and then use the first 2 days of it with a third assignment of players to symbols. Everyone will play together twice, and some pairs will play together three times. It is the most balanced schedule you can have.

Enjoy!
--Victoria