Now you are going to do some re-wiring to convert the 4xAAA holder into a 3xAAA holder with space for the LEDs. You have already removed the negative spring contact, but now you have to move the positive contact and red wire to the other end for your third battery. Take a thin flat head screw driver and pry under the positive contact until it loosens. You may have to also insert the screw driver vertically between the contact and the plastic housing wall to loosen it up the locking tab. See first picture
Then pull the contact and wire out of the case. See second picture
Now you will insert this contact and red wire to the other end of the case to complete the circuit. Notice how I am running the red wire inside the battery chamber.
See third picture
Now you will need to run the red wire to the corners like shown to make room for the battery. A small screw driver or thin blunt object helps. Be careful not to cut the wire or break the insulation.
See 4th picture