In reply to Souteril:
I called Tete Rousse in April and they said book online will be available soon. Since then I've been checking on the booking page frequently but no bookings were available for our date. I can't find any information on their booking page for the tenting. Gouter is also not available for booking. I think we'll end up doing the Italian route and either sleep in the hut or pitch a tent (from what I understand it's illegal to camp for over 48 hours so I hope tenting goes well)