Killing the motor noise requires putting the capacitor(S) DIRECTLY at the motor terminals. Even three capacitors, one from each terminal to the motor case, and one across the terminals. And likely significantly larger value capacitors.
Also, bypassing the H-bridge chip itself would be advisable
You can also put series inductors in both motor leads with a capacitor across both the motor and across the other side of the inductors. These should be larger than 3n5, make them 100nF and should be fitted physically as close to the motor as possible. One inch away is too far.
My next move was adding a very large electrolytic cap (3300 uF) parallel to the original, bringing the total to 3400 uF. For some reason, the Arduino didn't like that,