To solve the deformation problem I used a ~1mm thick piece of plastic (from the flash light packaging) cut and bent to fit over one of the Styrofoam rails of the helmet. This plastic spread the normally concentrated load from the zip tie over a larger area of the Styrofoam rail to where it would not deform.
Find some sort of plastic packaging that is fairly sturdy, here I show the use of a cookie container. Using the sharpie mark an oval appropriately sized to the area of the styrofoam you wish to protect. Then using some scissors, cut the oval out (see 2nd photo).
The third photo shows the load distributor in place. You will see how this works with the zip ties in a later step.