You don't say how big your filter is, but bigger is better and even though a change of cartridges costs more, your net cost of cartridges is less.
The water doesn't go through the tank. The tank is temporary storage to maintain pressure. It goes into the tank when pumping, and out of the tank when not pumping.
There is a solution that will help both your outside pressure AND reduce filter costs. Put a second tank AFTER the filter, and take your outside water from BEFORE the filter. Your existing tank with the pressure switch stays where it is, BEFORE the filter.
If you put the outside water line before the filter, you can backwash the filter by running outside water. You need to check to see if that causes a problem with the cartridge because they are not designed for significant backflow. If it causes a problem, then put a check valve right after the filter.
That does three things for you:
1. You are not filtering outside water, so the sediment that you would be collecting from the outside water is not using up the life of the filter.
2. You are cutting down on the flow rate through the filter. The first tank maintains pressure and continues to filter water at a lower rate when the pump is off. After a short time, the pressure on the second tank will equalize to the pressure in the first tank. The second tank will increase your pump cycle, which is good for the pump.
3. Your outside water pressure will be greater.
I would set the pressure switch range to the minimum that the switch will accommodate. Keep the top pressure where it is and increase the start pressure.
You need a pressure gauge on both sides of the filter. A gauge on both tanks will solve that if you put in the new tank as suggested.
The minimum that I would put in for a filter is a 20" long "Big Blue" size. A Harmsco HB-20-5W 5 micron cartridge lists for about $31.