From what we know, he began writing in the fall and was done with the first movement by the end of the year. Outside of a couple of conducting gigs, it seems like he has not been working on anything else. We are nearing the end of April. I would have to think that it is almost done.
I am getting the sense that it will not be premiered this year but next. Ax spends a good deal of time in Tanglewood in the summer. I wonder if Williams doesn't want to tinker with it with him later in the summer and then lock it for a premiere afterwards. Given that most symphonies have their schedules set by summer, I could see this most realistically as a Tanglewood 25 premiere.