Great work on the kinematics, though the pedant in me objects to absolute terms like "best" and "ideal". There are a variety of factors at play driving the shot of a ball.
Now, for extra credit, using reasonable assumptions for energy transfer, figure out how much spring potential energy your team's system needs to make this shot.
One thing I didn't see, but I'm too busy to compute - for what range of distances is the ball able to go in the goal?