If you flatten the variation (tighten the range settings), you cause the motor to start/stop more frequently. That wears the motor out and spins the electric meter. The switch manufacturers (probably motor guys too) want a minimum of 20 psi between the cut-in and out settings.
You should check/adjust your captive air pressure in your tank; assuming a bladder type tank. If so the air pressure with no water in the tank is to be 1-2 psi less than the cut-in setting on the switch. I.E. 30/50 gets 29-28 psi with no water in the tank so the bladder can compress fully and so you have the proper volume of air in the tank. Not having that right is the main cause of bladder failure.
To agjust the switch.. Depending on what type you have, the tall screw nut raises/lowers both the cut-in and out, changing the range. The short screw nut or bolthead (Furnas switches) adjusts only the cut-out setting. CW raises, CCW lowers.
There are no submersible pumps that you could use in a 2" well. Only sampling pumps are made in less than 3" OD. Depending on the depth to the water, and if you can get the stuff out of the well thats in there now for your current pump, you may be able to use a shallow well jet pump or self priming centrifical pump BUT... if the well doesn't produce more than that 3 gpm, that is out. Maybe it's the current pump that doesn't produce more than 3 gpm. If it's the well, then a new well is about the only choice or to connect 2 or more 2" wells together.