|Streamlight Rubber Strap Mount on firefighter's helmet, and Streamlight Clip Mount (inset).|
Streamlight, makers of industrial strength flashlights for fire and rescue teams has a good solution: The Haz-Lo Helmet Lighting Kit. In includes a clamp bracket so you can secure the flashlight to the helmet rigidly with a pivoting mount, a rubber helmet strap with holes you can thread the flashlight through, and a 3AA LED flashlight with a tail cap type switch. The clamp bracket has a captive screw so you won't be loosing those tiny parts.
More info at: www.streamlight.com/en-us/product/product.html?pid=283
A pair of these lights provides redundancy and doubles your work light to 240 lumens, each running 6-1/2 hours. Remember: It is still a good idea to safety cable the flashlight to your hard hat, and safety cable you hard hat to your gear belt.