I just looked at your data, the problem is that your timeline is non-linear (or has gaps).
To have a nice filling (-Sb?q+b), the points need to be evenly spaced (so you need to interpolate), or the width of the bars need to be adjusted to match the gaps (using gmt math -Q time.txt DIFF = for example).
Or you can be satisfied with small blank spaces, then your width could simply be 10/349 (plot width / number of lines) :
