IMO, she did not go down to the Refuge from the Pic. LE said early on that there was no evidence she went there. Indeed, she never said she was going to that particular Refuge. There are other Refuges in the area, including one at la Glère, that may or may not have had a winter room.
IMO the assumption/intepretation within the first days that ED went to the Refuge de V directly from the Pic has thrown a lot of people off, including perhaps LE/SAR. IMO there's no basis for privileging that route above others unless there was explicit, unambiguous, communication spelling it out. We haven't been presented with anything like that.
Phone signal, per the dossier, was good (though maybe not in patches?) in the Refuge de V/Hospice trail area. Maybe that whole valley (hard to tell exactly from the dossier). There was likely no phone signal in the P de la G area because of the lay of the land.