That is pretty good, too, and has a higher chance of getting an 8...
I am not thrilled about capping every score at 15 if you roll higher, though. Still, some more food for thought.
You can dispense with capping rolls at 15 and allow an occasional 16 or 17. It's a little easier and the average is 12.50 if you do so it's still within your desired overall average.