Preferably I do not want to go to the southern hemisphere, so where can you go in these months and still get some good skiing in?
Cervinia in Italy was very good this summer apparently. Warren Smith Ski Academy use it as their base for summer ski courses and were reporting fresh powder in June last year.
Saas Fee in Switzerland also offers reasonable skiing on the glacier as does Tignes and Les Deux Alpes though you'll only be able to ski mornings I think as the snow gets too heavy in the afternoons, at which point you can go mountain biking, swimming, work on your tan etc etc
Skied Hintertux in August - had a blast. They were skiing from about from the top which I think was about 3,200m to 2,600m. At the bottom went swimming in an outdoor pool afterward and finished up with pizza in Innsbruck to cap off the day.