When we talk radius of the platform are we talking dimensions of the box or the metal plate connected to the gear box?
I am talking about the box, unless the plate is significantly heavier than the box.
I guess my real questions is if the diameter of the gear on the stepping motor is 1 inch, does that mean with a 67 gear reduction the gear on my rotational shaft has to be 67 inches in diameter?
You can use more than one gear! As long as the losses don't build up, and the play/backlash is not a problem. Two gear steps with 10:1 ratio is the same as one gear step with 100:1 ratio.
Also, my suggestions are very much rules of thumb. And the rule of thumb is there to give you enough that you can achieve a reasonably stable movement with a reasonably limited change in spin (linear velocity) by simply applying torque over time.
As long as you have force to overcome friction (which can be made almost arbitrarily small for a spinning platform), you can use a weak motor, on the condition that you accept the very slow acceleration and deceleration you'll be able to impart, and you drive the stepper based on some synchronous feedback mechanism so you "know" when to turn on/off the different windings. You can use a 1:1 gear ratio (direct coupling) if you can get a synchronous feedback mechanism, and it will drive the plate at whatever the maximum possible acceleration is given the torque available.
Another warning: I'm not a mechanical engineer! I have a background in simulation software that simulates physical/mechanical systems, and mostly indirect exposure to the actual practicalities.
Love the picture, by the way :-)