As long as you're only running a 3s Lipo then you can just connect them up to your power distribution board.
And by connecting them you mean soldering red/black wire from LED to nearest ESC solder joint on the board? When I need to power something off of the board, that means soldering wires to the same point the ESCs are soldered to?
Still not sure about where to solder wires onto the LED, but I'm sure that and more will be apparent once I have it all in front of me. I do have a 3s LiPo.
Great article on your blog too. Maybe I'll use the HobbyKing LED with JST connectors you mentioned.