The New Year's eve phone call is repeated so often that it has to have happened in some shape or form, but it does look unlikely to have been the first out-of-the-blue contact that LB and SN had with FM at that point.
My hunch is that it was a formal offer, on the back of the informal agreement made at that Mexican dinner. Also, if you think about it, Christine had said her one condition was that she wanted to meet Stevie and see if they could on, which implies that there would have to be a point after the dinner at which everyone - including CM - gave their 'official' verdict. And then the formal offer could be made?
Mick's natural sense of drama leads me to think he would definitely not think twice about making that call on New Year's eve, too.
Loz