Thanks for the reply.

The ability to choose the time offset of x-scale would certainly be a useful feature in the future.

The scale draw was pretty easy and I've done my own class inherited from QwtDateScaleDraw.
I tried to do an own version derived from QwtDateScaleEngine, the only problem was when I adjusted the offset it got propagated to the plot with fake x-values which was a side effect I didn't want. I will try again but use QwtLinearScaleEngine instead. I only need alignment for hours and smaller units.