You could try a bit of heat shrink to help increase the width. Just be very careful applying the heat with all the plastic parts around it. I would probably remove the part that you need to apply the heat shrink to so as to avoid damaging anything with the heat gun.
The heat shrink is relatively smooth and not 'grippy' like the rubber band so it may have a better feel. Also if it doesn't work, the heat shrink is easily removed with a sharp knife.