The cheep water hammer arresters don't work good in applications where the pressure varies and become a vacuum at times.
You want a bladder style hammer arrester, also known as an air tank.
You also need a lot larger water hammer arrester due to the length of pipe inside of the unit. it's like running a pipe 100's of feet.
Given the "pilot servo" nature of the valve, there is no way to keep it from snapping on and off. (it's not going to fail, it's just the way it's designed)
The water hammer is best added after the unit and just before the solenoid valve.