I cut down to one tablet in the evening, for two weeks, then stopped altogether. Well I'm afraid the effect was not good: within a day my cough had gone noticeably worse. But I also very quickly got back into the pattern of waking up at 1, 2, 3, 4,or 5 o'clock in the morning and starting to cough soon after. So after two weeks of that disruption to my life and damage to my energy levels, I went back on the drug - and immediately felt better. My sleep improved the very same night, and my cough reduced - only a little, but significant enough to make it worth it. Two weeks on and I'm sleeping normally.
So I'm back on the morphine and I'll review that again in a year or so.
Incidentally, I'm about to retire from my job (as a university lecturer) and my wife thinks that the consequent reduction in stress could have a positive effect upon my cough, so we'll see.