I realize you have moved past the pressure switch as the culprit but thought I would add something in case you wanted to do a little extra preventive maintenance! It also may be useful for others searching the board in the future.

If you have your pump off doing other things to solve your problem, you may want to pull the pressure switch and clean off its diaphragm. Since you need a softener, you may have some deposits built up on there that over time could affect the operation of the switch. On mine it is pretty simple and quick to get it out, cleaned and then back in.

Our well water also needs a softener (and a house filter) and I had some pressure issues a while back that were solved by cleaning off the "crud" (technical term! ) built up on the pressure switch diaphragm.