I cut some raw potato ends and tried placing them between the bean bags and my neck. The potatoes were maybe 3" to 4" tall, and about the sharpness of a plastic Easter egg at the narrow end. The idea was to have firm but shapeable objects transmitting the pressure of the strap to the "sweet spot" where the carotid arteries come closest to the surface of the skin.
This did not work very well. The potatoes were slippery and could not be fixed in place. Maybe I should have used actual plastic Easter egg halves, perhaps filled with Great Stuff foam for stability…?