I've done it a couple of times -- the "Classic" version through Bourg St Pierre -- but never the Grand Lui variation. The first time was with Sharon -- because back then the HR was the about the only ski tour in the Alps for which we could find English-language guidebook info. Even that time we did not start out intending to do the whole thing, and I had previously done two of the best sections as independent 1-2 day tours. I didn't want to do it a second time, but it was what the American partners I was with had heard of -- so I went along to be sociable -- and even that time most of us weren't intending to do whole thing.

Nowadays there's no excuse any more for savvy ski mountaineers to be "doing the Haute Route", because:

(a) you can "skim the cream" of the best sections by just doing separately the "Three Cols" tour in around 1-2 days (from Argentiere to Le Tour) plus Arolla to Zermatt in around 2-4 days.

(b) the esthetic of the traverse accomplishment is spoiled by putting a bus/taxi ride in the middle (except for the Grand Lui variation -- which few parties could expect to finish in a week).

(c) there's so much excellent information available in English about the many other great 1-2 day tours in the western Alps which are equally or more spectacular and/or have lots better skiing:

Vanoise Ski Touring, by Paul Henderson (Cicerone, 2002) www.cicerone.co.uk -- The title doesn't do it justice. I see it as a collection of many of the best ski tours in the northern French Alps outside of the Mont Blanc massif.

Mont-Blanc Ski Tours, by Eric Delaperriere and Franck Gentilini (Editions VAMOS, 2000) -- All the ski touring in the Mont Blanc massif. Translated from French.

(d) There's so many other great multi-day traverses (for those who need that sort of thing) with English-language guidebook info:

Alpine Ski Mountaineering volume 1: Western Alps, by Bill O'Connor (Cicerone, 2002) www.cicerone.co.uk -- and volume 2 for the Eastern Alps.

Since those two times I've done various Haute Route segments and variations again [ photos | more ] -- and I'll be glad to do those yet again -- but I cannot imagine ever again doing the whole thing.