...The water softener is at our vacation house and we are not there now, so I can’t try the cleaning yet.
Hello Jane, my two cents here: Until I moved this year, I had a second home/vacation home, in central MI. The water there was significantly laden with iron to the point of being basically unusable (though many of my neighbors used it at their homes; why I don't know...low standards?).
20+ years ago we installed a MacClean chemical free iron filter. It did an "OK" at best job. However I can tell you that any kind of filtration system--be it a basic sediment filter, a water softener, an iron filter, or any other kinds of filters or combinations, do NOT like to sit for extended periods of time. They will eventually give problems and or reduced performance.
These things are designed for FLOW, not stagnation.
With the occasional use of our weekend home, we had to perform a number of things to that system annually to keep it working "OK".
Then, in August 2019, we moved to the house temporarily until March 2020, so we were in the house all the time, and using water all the time.
That iron filter was now working daily, and can tell you that with constant use the water quality improved significantly.
Even with relatively iron free water, it still wasn't good enough to drink (taste wise), so we installed a small five stage RO (reverse osmosis) system under the kitchen sink to supply drinking water and water for the ice maker.
If you are not at your vacation house all the time you may want to rethink the usage strategy. Just a thought...