Groulx actually pushed Price to play more like Quick this year (constantly on his knees) and that's most likely what led to his firing. (Who's decision it was to change his style isn't sure, but Groulx did coach the change)
No point in trying to change a goalies style IMO. Work with what you have.
Quick's style isn't always on your knees. That was what Groulx/Price came up with in the off-season and it is absolutely BRUTAL. I yelled about it in many threads, it just does not utilize ANY of the proper theories of goaltending nor does it allow Price to use his brilliant lateral movement to his advantage.
Quick's theories come down to this: Puck's eye perspective. The puck has a different view of the net than the shooter. The closer to the puck you become, the less of the net the puck the sees, and also the steeper the trajectory of the puck must be to reach the upper portions of the net. Quick crouches lower and lower, upper body becoming tilted forward to the ice the closer the puck comes, he also gets out on top of his crease. If the puck is passed or shot wide, that is when the strong legs come in handy, quickly rotate and come back to your post, set and read/react to the play, come out aggressively again if the situation calls for it.
When the puck is below the goal-line, only when it is directly in the middle, should both legs be down in the butterfly position (on your knees) so that if there is a quick stick move, they can't get the puck into the near side post. Any time that the puck moves beyond the center point of the net, you have to load the post side leg (plant your skate on a strong angle into the ice and activate your muscles to be ready to push), and be ready for any quick pass plays that may go into the slot or across the net, or shots generated for rebound opportunites/crease crashing.
Quick gets into the splits a lot during recovery situations because most of the time, the puck is close to the net, so he knows if he gets his legs wide, the low posts are covered and if he leans his upper body forward/reaches to the puck with his hands, he can limit the areas he can possibly be scored on which allows for a lot of acrobatic saves to be made.
If we get Allaire.. you will see Price get into shooting lanes, react to the shot or the sound of the shot, get down into the full butterfly, maybe center shift (lean your torso into the direction of the shot to eliminate holes) and rely on his defense to clear away rebounds or tie up their men (which is what Ottawa did to us). You will not see a lot of movement with Price, you won't see him making dynamic movements, it will be all about playing percentages and relying on them rather than reading, reacting and using Price's athletic and biological gifts to his advantage.
Dislike Price for his lack of intensity? You'll hate him even more under an Allaire teaching syle because it will take mostly all of it out of his game, turning him into what we saw of Reimer for most of his career, a robot who gets in the lane and is never in position to make a second save and is never fighting through traffic or screens to see the puck because they are more worried about filling the lane with a percentage blocking technique than analyzing the situation.