I spent a full week in La Grave 2 years ago; it’s a great resort and a great ambiance, people are very genuine there and love and respect the mountains. However it is very demanding; some of the rides are not too technically difficult but it is very physical. It’s a high resort, the cabin takes you to 3200m and the first day you will struggle breathing at the top.
You can never rest...as you entionned, no slopes, always tense. The guide will tell you the first day, “you don’t fall in La Grave”.
Forget about the connection with les Deux Alpes, you have to walk 20 mins at the top of the resort, and if you miss the last one you are in for €150 taxi, not great.
Mistake I did was not to invest in massage after 2 days, my kegs were burning. If you go, you need to approach it as serious sport, not leisure.
That said, it’s probably the best week of ski I ever experienced, not busy, great guides, great food; the key is to be in good (very good) condition.
I went with snowlegend.com, talk to Didi the boss he is a great guy.
Let us know your thoughts when you come back.