I was able to put together a separate box to hold a 8xAA battery pack, which attaches nicely to the back of the GoGoFuge (as shown below). The GoGoFuge can be powered by this battery pack or a 12V wall adapter. (Also notice the super cool Dremel wrench holder on the side of the GoGoFuge):
The innards look a bit convoluted, but they involve only three electronics boards (GoGoBoard, Relay, and Display) and a total of four buttons. Also, as you can see below, the "Motor Lock" button on the back extends to the motor lock on the actual Dremel, and is held in place with wooden rings of various diameters (one with a hole in its side for the locking rod):
In the end, the safety switch (located ontop of the interior display board) worked well and was activated only when the lid was closed, thanks to the acrylic protrusion on the front of the lid:
In addition to the spinner attachment, I also made a jiggler attachment that can be used to vortex your liquids (i.e. mix them up), which is comprised of both laser-cut and 3-D printed parts. It features and radially free tube holder (laser-cut acrylic) attached to an off-centering dremel-rod holder (3-D printed). The attached elastics secure to the GoGoFuge to prevent the tube holder from spinning.
Here is the jiggler bit locked in place in the dremel:
In the end, I was very pleased with how it all turned out. Thanks to help from Ripul, I was able to display the "Time Remaining" once the GoGoFuge starts, including the minutes and seconds. The GoGoFuge then resets once the run has completed. Yay!
I should also note that I compiled my drawing files so that they can all be done using one run of the laser cutter, as shown below: