Some Comments
Kudos for all this work.
Couple overall comments. First, the rink effects on shot locations are nonlinear so that the mean adjustment is generally inadequate for rinks. Might want to look at the Total Hockey Ratings (THoR) paper of Schuckers and Curro to see another possible adjustment. Second, as others have noted there is very likely a team effect (outside of rink) in your ratings that will need to be accounted for. You also should take a look at the Expected Goals model of Brian Macdonald as reference point for another expected goals model. Third, it was very nice of you to do the year to year correlation. More years would be very useful, especially considering that 201213 was a shortened year.
The reason that shot quality (which is what you're after here) is not utilized more is that its effects have been fleeting. I'm not one to total exclude the effects of shot quality (or average shot probability) but skepticism in this area is well warranted.
Some technical details: Wilson's BPCI is not the one you want here (it's not appropriate for the type of data that you have) nor is it the one that is used in political polls. A (Bayesian) alternative would be to take (EGF + k)/(EGF+EGA+2k) where k is some number such as k=5 or 10 which would 'shrink' estimates to 50%. You might have to select k based upon a full season rather than on '12'13.
