How to create clusters of position data?
I doubt any of the clustering algorithms will work well.

Instead, you should look into:


segmentation (yes, this is something different), specifically time series segmentation
change detection (as you said, there is a rather constant distribution first, then a change, then a rather constant distribution again
segment-wise regression may also work: try to find the best fit that is constant, linearly changing, and constant again. It's essentially four parameters to optimize in this restricted model: average before and after + beginning and end of transition.