Does it say which cree is in that? If it's not an r5, xml, or xpg, I wouldn't bother. It looks like the actual lumens listed is honest. Also, I'd recommend pulling them apart and lock tightening them together. I've had seveal things of similar quality/price.. rattle apart! These are a temping set up
Also, battery run times are not linear. a 6ah battery should be able to provide 6 amps over the course of an hour. In this case, your going to be pulling 36 watts. 36/12=3 amps. If your lucky, this may yield more than 2 hours! The later half of the 2 hours may have so low of a voltage, the leds won't light.
Anywho, I've gone through this situation numerous times with my rides, Typically old 3 wheelers with no regulator at all!. At least the blaster regulates to 12v AC. AC is very very very easy to convert to DC.
Unless your looking for extended run times with the battery, I'd forgo it for a different storage medium. Would something that gives you 30-60 seconds worth of juice(while the machine isn't running), never craps out when it goes to 0 volts, charges within 5 seconds, can be discharged and recharge over a million times sound good? It also weighs considerable less than the battery. non spill-able and no threat of it leaking or expanding. zero maintenance... With the exception of run time, it all sounds great. Look for ultra caps.
Ok, So the magical AC to DC component is a diode bridge. It rectifies AC to full wave DC. It's the simplest method. It does not regulate voltage. 2 AC wires connect, then a + and - exit.
http://www.ebay.com/itm/Bridge-Rect...457431?hash=item3f57e35b17:g:cD8AAOSwBahVbRkX
Instead of a battery, I'd look into a Super capacitor bank. This one will provide probably close to 3 minutes of continus run time.
http://www.ebay.com/itm/16-Farad-16...458225?hash=item3d201824b1:g:y6kAAOSwmtJXZTCr. They get much cheaper, but that is one of the best bangs for the buck (i didn't know when i bought mine
Now due to the voltage regulator, and the DC rectifier, you can get away from the battery all together. You won't have any lights while your not driving though. My estimates of the run times with caps I based off personal experience with a 5 F bank and a 233F bank. Capacitance does not add up in series, it actually lowers. That's why your seeing a 100F cap bank rated for 16F. A 58F bank will run a couple of HIDs for nearly 2 minutes. Super caps are similar to capacitors people put in their cars for high end audio. The difference is that these are newer technology and have about 100 times the energy in them that a car audio cap does.
This should work as a replacement.
http://www.ebay.com/itm/1-3-Farad-6...218524?hash=item567cb1dc5c:g:fxMAAOSwo6lWFnGw