Try measuring the voltage at the battery pack rather than the light -- if the voltage is higher there, then the problem is your long wires.

That said, while I admire your DIY attitude, I have to point out that a single cell 18650 flashlight would probably beat your system in most ways, and can be had with batteries, charger and light for around $30 or maybe less. It would be a lot smaller and more convenient, put out more light (on high), and last longer (on medium, which would still put out about the same amount of light as your system.)

Actually, the Amazon light mentioned recently is an even better choice.

And to answer your question, 18650 is a size, like AA or AAA is rather than a rechargeable or not-rechargeable designation, but I've never seen one that wasn't rechargeable.