Unfortunately, something like
xl=ax.XLim; % retrieve current limits
xl(1)=dateshift(xl(1),"start",'minute'); % round down for first
xl(2)=dateshift(xl(2),"end",'hour'); % up for second
xl1=xl-xl(1) % convert to duration extent
ax.XLim=xl1; % redefine axes as duration
doesn't work; I've submitted enhancement request for the feature previously but so far, no joy.
I have found no way to force one into becoming the other; one has to redraw the graphic to make the change.
Probably the most direct way in your case would be to write a translation routine that does something like the above from the existing figure and then redraws it rather than fixing all the pieces individually, at least as a start.
