I've been using a Fenix BC21R headlight for about three years now. It's 880 Lumens on high setting, which will run about 90 minutes.

The really excellent feature of this light is that, although it's rechargeable though the port in its underside, the battery is not permanently sealed in its body; you can unscrew the back and swap it out for a fully charged one, letting you ride long hours. I bought an extra 18650 battery and a charging dock so I can leave on rides with 3+ hours of full brightness.

The down side is that the handlebar mount isn't a proper clamp, but rather the type that uses a rubber strap. It's okay for smooth conditions, but probably wouldn't be adequate for off road.

Not sure if 880 Lumens is enough for your needs, and with your budget, you may be able to find something brighter, but I thought I'd mention this as it's been a good, solid, well-built and well-featured light for me.