I like the matrix idea. How about different matrices to choose from? You could name them.
The all-around hero: 7, 8, 10, 12, 13, 15
The overly specialized: 3, 9, 10, 11, 12, 18
The average Joe: 11, 11, 11, 10, 10, 10
Mr. Extreme: 4, 4, 4, 17, 17, 17
I would have the average hit 63 or whatever the average roll is.
I would not allow for point movement. It's too fussy. If I were to choose a matrix, I would just want to be done with it.