OK.  I've been playing around with my LEDWiz and reading the directions again and realized I've been way overthinking things.   

  I do that often.  LOL.  But in the picture you first posted just move the wire that you have in the ground terminal to the +5v terminal next to it.  Should work fine after that.
I would use a terminal strip similiar to this one.  
http://groovygamegear.com/webstore/index.php?main_page=product_info&cPath=69&products_id=201You can hook up the +5v from the LEDWiz to it on one side and daisy chain it down that one side, then just hook the +5v lead from the LED's to the opposite side to supply it with 12 volts.  Will either need 3 of them for your 32 LED's or just put 3 LED's in each of the terminal strip ports.
Also 32 LED's will have you over 500mA if you are using the USB's power.  For single color LED's you are at 640mA (32LED's x 20mA).  If you are using all RGB LED's then you would be at 1920mA (32LED's x 60mA) as each LED is basically 3 LED's in one.
Took some pics that might help.
1st pic - Everything wired up.  All connected to the +5v off the LEDwiz.  Port 1 is Trackball Red, Port 2 is Trackball Green, Port 3 is Trackball Blue, and Ports 4,5,6,& 7 are single color blue LED's.
2nd pic - A closeup of the trackball RGB wires.  For clarification ?.  Not sure what I was thinking with this one.   

3rd pic - A closer view of the single color Blue LED's wires. 
4th pic - Everything lit up and working.  I daisy chained the +5v from the LEDwiz to the LED's but since I don't have a terminal strip yet I just twisted the ends together and used a short wire with a clamp on the end to connect it to the LEDwiz.
I'll make a vid later today or tommorrow if you need one.