Just to throw out some basics here:
1. Puck behind the goal line= goalie hugging the post keeping the rest of his body along the goal line/mouth.
2. Puck comes across the goal line= goalie square to the puck. (Unfortunantly when you keep getting burned by the back door you have a tendancy to start cheating.......then you get burned by the first guy.

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If there is the possibility of of actually getting across in time to make the save, the goalie has to be able to anticipate the pass, and have explosive enough moves to get across in time......concentrating on squaring up with the shooters stick, not the shooter.
Another thought along these lines is- When the puck carrier goes deep into the corner, this is the time that the goalie can "look off" of the puck to get an idea of where every one is positioned......especialy the back door shooter( Taking note of what hand shot he his.)
In reality, this is actually a "D" problem not really a goalie problem (which you have already stated.) It seems to me that it would be easier to instruct the D than I would be to try and get the goalie to perform a miracalus save.
A simple "D" plan:
Two D men back, the puck goes into the left corner, the left D goes to it and the right D stays in the slot tying up any sticks that might be there(This would include the backdoor guy, Let the forwards worry about the point guys breaking in) . The opposite is true when the puck goes into the other corner. If the D that stays in the slot tries to position himself between the puck and the backdoor shooter in hopes of intercepting a pass, chances are the pass will get through, and a goal will result. If the backdoor shooters stick was tied up, there is no chance of him getting a shot off. The plus side of tying up the shooters stick is that your own D will not be able to make a niffty deflection into your own net! (Man that really burns me up!!!!! )
Hope some of this helps.
Rick