In reply to _northern_ray_:
I have been to Gran Paradiso many times and am walking part of the Alta Via 2 in late June (the other direction from Pina through to Höne, then train onto Ivrea & Locana and up into Gran Paradiso) for my 50th!
What I would say is that there are quite a few empty hotels and a few permanently closed refugios these days and that in some areas e.g. the more popular resorts like Cogne, the hotels do tend to be more pricey. I think the summer season is more than bookable, but what is probably more of an issue is not enough accommodation and lots of people visiting as Aug/Sep are the peak months. Best best friend runs a B&B in Locana and I know that she is already 50% full!
With quite a bit of wiggling about, I managed to find accommodation between 25 June and 3 Jul through a combination of Booking.com (where I booked all of them for free - payment not taken till early June, so wiggle room there if needed) and then an email to the refugio (Refugio Miserin were very quick and helpful and I just paid a 15E deposit and it was done).
I am not sure there is much to choose between the two routes - both have lots of very decent ascents and will be spectacular to walk in terms of wildlife, and nature etc., I have made up my route purely because I wanted to start in Aosta (cause its such a fab place with all the Roman remains!) and finish in Gran Paradiso because I have many friends there. I am happy to share my route with you if it is of any use. There are lots of other paths which join up with AV1/ AV2 that you could use to take you from the Aosta Valley through to Gran Paradisio, ending up in Ceresole Reale. It all depends on where you want to fly to/ from.
What budget do you have for each night? More than happy to recommend places for you.
Claire