Sam,
I'm not going to attempt to diagnose the spotting issue in your photographs, but just relate my recent experience of returning to black and white film processing at home after a gap of very many years. At my current location I was forced to use unfiltered spring water with the potential for chemicals from agriculture to be present in the water, as well as solids in suspension. The water is also very hard, in other words it has a high lime content and compared to my previous experience with soft, filtered town mains water, the results were very disappointing, both in terms of marks on the negatives, probably due to solids in suspension sticking to the film as well as uneven development and poor contrast issues. Given the high lime content the pH value of the water will be relatively high and might alter the behaviour of the developer, I'm no chemist so I couldn't comment further.
My old copy of The Ilford Manual of Photography suggests that water quality is normally not an issue and that tap water is a satisfactory alternative to distilled water, however I think that in both our cases the use of unfiltered water has a great part to play in poor results obtained. I'm afraid that I haven't done anymore home developing so can't add any further thoughts. I'm sorry to be a little discouraging in my thoughts.
Again The Ilford Manual illustrates defects in negatives and scum in the water produces white spots on the negative that would result in black spots on the print, so actually the opposite of what your prints show. That might point to dark spots on the negative caused by dust particles when scanning.
Barrie