Just a quick post today, as I'm about to go out to the theatre.
But good news on the dishwasher front! I eventually called the manufacturers, who sent along a Man. The Man pressed various buttons and water rushed around; he looked under the sink and twiddled the outlet hose.
And he announced that probably the problem was the way the outlet hose was fitted to the 'space-saver' waste pipe under the sink; that he'd altered the angle of the bit the dishwasher hose was attached to, and used some 'cable clips' to keep it in place. Then he drank a cup of coffee ["Two sugars and milk, thank you very much!"] and left.
And hey presto, the next wash we did there was NO grey scummy water sloshing about in the sump, just about a teaspoonful of clear water at the bottom. Hurrah!