This kind of thing is possible starting in eastern Turkey and continues in the rural areas going east. I don't know about security, is probably ok, who knows. But you should do it now, don't wait.
Thanks Sitkack, I have four children. So my adventures are on hold for a bit, and while the risk of this journey may be increasing year on year, in 15 years when the youngest is an adult, my willingness to take on risk is going probably go back up quickly. What I'd really love to do is travel east to west and cross into Mongolia. How important is the radioactive contamination from nuclear testing in along the border?