Did you need to make bookings at the rifugios? It sounds like weather is likely to change one's plans as one travels this route. This trek has been on my list for a long time so it's fun to read about it. I wish you posted photos too!
Yes, you do - at least in peak season (though there were a few spare beds at the one I was on on the middle night which were snapped up by wind-blasted intending campers). The configuation of the tracks, though, means that there are quite a few different ways you can do things with a set combination of overnights.