In reply to jameshall:
We did it east to west which I think is the norm and bived all the way. Have done quite a lot in the Sierra Nevada generally and know it well.
The Caldera refuge has been restored and is in good nick. It was clean last autumn. However when we last planned to stay there, we got settled in, climbed Mulhacen and returned to find a school group had arrived for the night. (We packed up and bivved elsewhere).
The Poqueria refuge is a top class hut with bar and restraunt service. It is a bit off route and we didn't use it on the traverse.
The Valetta hut is as the Caldera refuge in terms of being restored and o.k. However as it is nearer the roadhead / ski resort, it can be busy or full.
The section between the Valetta Hut and Eloretta is quite scrambly with interesting route finding.
The Eloretta hut is a stinking place.
The Cabio hut was clean at Easter.
Late September can be either hot or extremely cold. We had an extremely cold day on Cabio in September two years ago. When we did the traverse in July two years ago, one of our bivvi's was on an exposed col and there was frost on us in the morning!
If you want to chat about it, e-mail me.
good luck.