You need pressure gauges on both sides of the Culligan system, and ideally, between each element of the Culligan system. Without gauges you have no way to prove what element is causing the problem. I would deal with that before doing anything else.
The Culligan system probably has inadequate flow capacity or too many pieces that are causing pressure loss. The best fix is probably to add flow capacity (larger tanks) or get rid of some elements if they aren't really needed.
If you don't own the Culligan system, then you might consider getting rid of it and putting in your own system that is sized for the requirements. There are people on this forum who can help you with that approach.
After you have identified the factors causing the pressure drop, you can decide whether the problem can be fixed within the system, or if you must do something more drastic.
If you require all of the elements in the system, and can't avoid the pressure losses, then you must set up a system that will give you satisfactory performance with that system. That involves applying some engineering to determine what must be done to meet your requirements.
My solution, after doing everything possible to reduce the pressure loss in the Culligan system, would be to put the pressure tank AFTER the treatment system. (That suggestion will cause a small explosion on this forum, but it WILL work.)
You are apparently operating as high as 80 psi now. Here is a system that will work, but before selecting components I would want to know the make/model/capacity/pressure of the pump. An oversize pump will make the problem more difficult.
Install the equipment in the following order:
Pump --> Cycle Stop Valve set at 80 psi --> Relief Valve and alarm pressure switch --> Culligan system --> Pressure tank with switch set at desired operating range
The pump will operate based on the pressure switch settings at the tank. The pump will deliver water to the CSV which will regulate the pressure but will allow about 1 GPM to finish filling the tank if the pressure on the inlet side of the Culligan system reaches 80 psi.
The tank will deliver water to your household without the pressure losses in the Culligan system, as long as you have enough storage. Therefore, I would install at least an 80 gallon tank (or multiple tanks with total capacity of at least 80 gallons). Sustained flow will still be limited to the capacity of the Culligan system.
The alarm pressure switch will alarm and the relief valve will discharge to waste if the pressure exceeds its setting, perhaps 90 psi. You can set up a relay system to shut down the pump when the alarm switch actuates. You should have at least 100 psi capability of all of the vessels in the system, from the Culligan system to the pressure tank.
You will need gauges on the system to determine where there are problems if the Culligan system gets plugged, and you will have to inspect the system when it is running to determine if there are problems.
Owners of wells with treatment systems must learn how they work and how to operate and maintain them. Otherwise you will enrich the well/pump service companies with your frequent service calls. That is part of owning a house with a well.