Quoted from lyonsden:I haven't tried to do this, but this looks like it would work: ebay.com link » Ac Dc 5 35v To 3 3v 5v 9v 12v 24v Buck Step Down Converter Volt Linear Regulator
Note that the output is 600mA at 5V, which is enough to drive 30 single color LEDs
This says step down regulator where you need a step up regulator to go from 6,3V to 12VDC. Like
ebay.com link: 0
And yes, you will need to set a bridge rectifier with a small Elco between the GI and Input of the regulator. Done this several times and no problem for small amount of leds. Also note that if you have replaced GI bulbs with leds this frees powerbudget to add extra leds without straining the existent power source.