My solutions:
1.) Simply the cut a ribbon and an extension sew in between, then it fits the thickest "pear".
2.) Since I'm mostly without a helmet, only with cloth hat on the way, I have the two Velcro straps, and the adhesive plate away and sewed the remaining Schraubträger on my hat with a needle and thread to the 4 corners of the joist. On slippery road are so ordinary video feasible on cobblestones and forest trails not. If the hat has to be washed, I put the easy part with the support in the machine ...
3. With a little tinkering is in a similar manner, a fastening the helmet possible - not only with twine, but with screws, washers, nuts and 4 drilled holes. For this drill well holes in the adhesive plate. (No screws through the slots of the support screw) - these turn up and break before a sufficiently firm screwing is done.
-Micha-