Obviously one of the first things I looked into was costs and timings. Unfortunately it seems that my window of opportunity (the latter half of August) coincides with the end of monsoon season.
So I can look forward to leeches, rain, and possible landslides and bridges washed away.
Also, there are very few organised treks at that time of year. Obviously.
Also, in my original plan, I was going to fly to Beijing then get trains to Xian and thence to Llhasa so that I could combine my love of great train journeys with a 3 day acclimatisation to the altitude. Brilliant plan, right? Well, it's a good thing that I'm doing a great deal of research because I discovered that they pipe extra oxygen into the train so I would still have to get used to the altitude at the end of the journey. Back to Google then.