I've found this method (see diagram) to be very effective:
It's an X pattern, but with an arc.
Just something you might want to give a try. Oh, and you'd start the stroke with the point (toe) where the red line begins (the razor perpendicular to the strop or slightly angled opposite from the final position shown) then follow through, as diagrammed, with that arcing, or sweeping stroke as shown. Kind of like a wind shield wiper.
And, the razor doesn't fall off of the strop. You'd do your flip at about the spot where the diagram shows the razor resting at the end of the stroke, and then start the second stroke at the beginning of the other red line.
Hope that's not confusing.