Tod77. No! the small pressure tank will not aleviate the pressure fluctuations.
The pressure tank is supplied because water will not compress, the tank allows the pressure to expand into the pressure tank thereby giving you some drawoff before the pressure reaches the bottom switch setting.
Install the Pressure reduction valve on the outlet side of the pump after the Pressure tank & set the outlet pressure after the valve to slightly less than your bottom switch setting.
Good luck, Bob