We have a new winner. And as silly as this sounds, the winner is Smith & Wesson. Really. Have a look at this:
And get this: My total cost was only $19.99, including shipping. Here's the puppy, the "Smith & Wesson 3-Watt Cree LED Head Lamp."Yes, it's a headlamp. But that adjustable head strap wraps nicely and securely around a handlebar to provide a snug fit on a bicycle as well. And as the picture shows, it's miles above bicycle-specific LED headlights that don't require special batteries. (This was a requirement for me because nighttime randonneuring called for long run times without recharging. Spare AA or AAA batteries are easy to carry, and they're almost always available at nearly any convenience store.) It's also considerably smaller and lighter, another bonus.
I haven't tried a full-nighttime ride yet, but I did have it out after sunset tonight, and it clearly was superior to the lights I'd tried previously ... and at about one-third the cost.
