There is flash HSS in photography which does not mean High speed sync. I use it on my 6d and can shoot at 1/4000 with flash for personnal shots. Of course, I don’t use my 6d on my drone because it’s too heavy.
With Sony hybrid camera, if you put your camera in manual, you could use fast shutter speed and still get hot shoe signal (Watch here : Sony NEX-6 sync-speed test with Cactus v5 wireless trigger - YouTube ) which is important for geotaging. But as far as I know, your QX1 doesn’t have manual mode and no hotshoe option