The problem is that your rheometer is shear stress controlled, so when you ask for a shear rate, or strain, the instrument has to use a feedback loop to give you what you want. This task can be very difficult, depending on the sample rheology, as your results demonstrate.

I suggest thinking about exactly what rheological data you want and then trying to find a way to obtain it using the rheometer's stress control directly, e.g. with creep tests or shear stress ramps. This way you will always get what you ask for.

Good luck!