if I need to carry the munoz a long way, I use a simple shoulder strap that I made from an old seat-belt, dead easy.
One place that a strap type handle would be good is on either side near the front to grab when you esky. One of the problems I find is when I manage to find myself just in from the impact zone where it's too late to bail and dive and an esky roll is my only option, it's really easy to lose a big board by having it ripped out of you hands.
Then you're at the mercy of the wave because you're being dragged along inside the foam ball by your leggy wishing you had not smoked so many cigarettes before you turned 50