Just playing around:
Was looking to reach the target before the arm gets there:http://FantasticContraption.com/?designId=504246
It puts a backspin on the target, but the long reach of that arm still easily grabs it.
Tried a heavier arrow:http://FantasticContraption.com/?designId=505315
That one blocks the arm and gives the target a good whack if the arm is gone, but it's still not enough to knock the target towards the right goal.
Tried a wheel:http://FantasticContraption.com/?designId=504820
Also knocks the arm and also gives the target a good whack if the arm is gone. But there's no "billiard" style deflection when the wheels hit, so it seems the target can't be knocked to the right side enough to win against a wall push.
Onto next idea.