I suggest you to build your own WP_Customize_Control
class that does exactly what you want. You can copy-paste the core WP_Customize_Image_Control
code on your own class and modify it to fit your needs.
You can follow Otto’s guide to create a new control.
I personally use the Customizer API to modify the background-position
CSS property of the background image using the mouse dragging movement (see the git repo).