March 2014 to August 2018 isn't exactly going out on a limb in narrowing down a prediction.
The conclusion is "I have no idea" and "whenever he damn well pleases".
My guess is that The Winds of Winter
will be published no sooner than summer 2015 and (hopefully!) no later than early 2016. Some of the climatic moments delayed from the end of A Dance with Dragons
to the beginning of Winds
will probably be seen on screen before they're published, but at least fans will be able to read most of Winds
before the material airs on the TV show. I think A Dream of Spring
will only be published in the early 2020s, while the TV show will end in 2017 or 2018.