Other than layout of the circuit board (which always seems to take days), the packaging and fabrication has been the most time-consuming part of the project.
Of the original stir plate purchased on eBay, the only part that appears in the final machine is the cast aluminum housing. However, this piece has been crucial and nearly all of the mounting bosses have been utilized. All of the original holes for the controls and indicators were filled and new holes created for the switch, the rotating vertical rod and new power cord. The housing was then sanded, primed, and painted with Hammertone finish.
The bearing carrier for the vertical rod and its integral servo mount were built to fit four mounting bosses already present. Likewise, a sheet metal bracket was modeled and unfolded in SolidWorks, then fabricated using a simple "vise brake" bending tool (thanks to Brian L). This was also bolted to existing mounting bosses and doubled as shielding for the switching power supply and a mounting surface for the Arduino, which is rigidly mounted with its USB port existing the back of the housing for ease of programming.
Of the Sunbeam HotShot, only the stainless burner assembly remains, and even that has been trimmed down because the water reservoir will be a polycarbonate tube, in keeping with the "translucent" theme of the project.
The burner surface was replaced with a custom-ordered square of tempered glass with turned aluminum standoffs. Even the feet are custom-made.
There is barely enough room in the housing to fit everything:
This view from SolidWorks gives some indication of the density.