In reply to Tricadam:
Have you considered the Pyrenees? They tend to be a lot quieter than the Alps, although as has been said the August holiday period is about the worst time anywhere. Also there is an increased risk of thunderstorms in August. The Gavarnie area can get busy, but the western end of the chain, eg AspeValley/Cirque de Lescun, can be a lot quieter and has some beautiful mountains. Unlikely to be snow there in August but some good scrambling. No lifts I'm afraid - but that's an asset because it keeps the crowds away! Great high wild camping near mountain tarns.
Corsica is also beautiful and relatively quiet away from the GR20. Magnificent granite mountain scenery, lots of good scrambling, but snow unlikely in August, although the same comment concerning thunderstorms.
Off topic, but how refreshing it was to see you open your post with "A friend and I...." rather than the UKC's usual "Me and my friend"