Simple answer is don't auto-detect. Allow the user to set the scaling factor per screen and then just auto-apply that when using that screen. This just requires a way to uniquely identify screens and requires the user to set the scaling factor for that screen once when first used.
Initial autodetection and scale-factor setting is ok. Otherwise most regular users would just say "all my icons and text are too small on my new notebook". Windows detects the high dpi in that case and sets the scalefactor to 200%, which gives a good starting point. Of course the user should be able to override this permanently if it isn't his preference.
