Thanks, that's great, it seems to be working as it should finally.
I did the soap test, and the newly treated water foamed up much more, indicating that softening is taking place, so that's good too. I have somewhere I can take a water sample in for a quantitative test, so I will do that in a day or two.
The only question remaining is to ask why did it happen, and will it happen again? The original problem was resin beads stuck in the drain flow control thingy, as well as quite a lot in the drain pipe itself (an accumulation over some time I expect). And these didn't seem to be broken ones, they were spherical as I found when I put my foot on some that were spilled on the floor and went skidding away. Is it normal for some of these to get expelled from time to time, and if so what sort of preventative maintenance regime is advisable?
As far as the black sulfide is concerned, Culligan's advice is to increase the backwash frequency in the Iron-Cleer water filter, so I will do that and hope that over time the inside of the softener will clean up.
I really appreciate all the help and advice, as without you being there to guide me I would never have got this far. I have also learned a lot about my softener in the process. So a big thank you.