There are two reasons for a light. The first is to have it so if a ride goes longer than expected you are not stuck out in the dark. This kind of demands the stator so it's always there. The second is because you plan on riding at night. Batteries will do here.
If you must go with batteries, consider the bicycle lights. They are basically equivalent to the 2x2 LED lights you mentioned. Since they are mass market they are cheap and are surprisingly bright. Way better than what comes stock on most dirt bikes with an OEM headlight. I use a couple as helmet lights they are amazing. I can easily ride with just one on my helmet. I have a HID on the bike, but I tried shutting it off and the helmet light is enough. No reason you couldn't mount one on the bars or something.
I have a dual LED light and I'm going to adapt it to a GoPro mount. That way the helmet mount is for videos during the day and lighting at night.
You can get a kit with the light and battery for around $20 and standard capacity 2 hours on high spare batteries start at $10. You can get larger batteries that run on high for at least 4 hours for a bit more.
Dang the prices keep falling. Here is a dual for under $20. Says 5000 lumens, but more like 1500 for real. That's about like a car headlight.
http://www.ebay.com/itm/New-5000-Lu...319?pt=LH_DefaultDomain_0&hash=item3f37e8d4a7
Can't go too wrong for that money.
Lithium batteries hold their charge for at least a year do as long as you remember to bring it along it will be ready should darkness fall.