Just a tip which will help you get around cost and availability; every year our family and our friends from the UK book our holiday through a British tour operator (not always the same but we have used Peak Ski, Inghams and Snoman.co.uk).
It's cheaper, you get half board, two students to cook and clean for you and you can usually get a really great chalet close to the lifts.
You can even make the booking from Switzerland (it usually falls to us anyway because we are the most organised

) and you just get the company to knock off however many flights and transfers you don't need.
In the past we tried to set everything up ourselves (find an available chalet, set up flights for the others, do enough shopping for a week, arrange ski passes) and it's just a big overpriced pain. Now the holiday company does it all for us and we just turn up on the Saturday afternoon to a nice clean, warm chalet and usually tea and sticky buns.
Verbier is great, by the way.