The idea sounds perfect for an inspired tinkerer.
But…Tom and Ray: why didn’t a discussion of lubrication for the transmission come up? Transmssions typically are splash lubricated and standing it on end would create 2 problems:(1) the output bearings and gears would run dry and (2) the input seal is not intended to seal a sump, but to prevent splash lubrication from leaking.
To make this a practical solution wouldn’t the lubrication have to be replaced with grease, or would a right angle drive have to be attached to the output end?
Some would question MIT mechanical engineering. But I wouldn’t dream of such a thing… 
I was in an OLD machine shop over 30 years ago that used overhead line shafts to drive flat belts to propel some of the machinery. There were some machines, I think mills of some sort, that were stepped down in speed and upped in torque by the use of old common ordinary three speed automotive transmissions. The transmissions were standing on end, output end down. I commented to the guy showing me around that it seemed as though they’d leak. He said they sometimes dripped a bit, but a new output shaft seal would always fix it, and oil dry was cheap. They were filled with 90 weight, as full as the fill plugs would allow. He said they had been there like that for many years. I suspect that the original owner figured it was far cheaper to use salvage yard transmissions than to buy expensive purpose built transmissions. If one wears out, just go back to the salvage yard.
Just remember, neither of them have engineering degrees, mechanical or otherwise.
Lets not forget that the transmission would only be used as the speed controller. The stand, top, wheel, shaft, pillow block bearings,coupling, and motor all still needs to be built or obtained. Having said that it would be much easier to just buy a inverter rated motor with correct rpm and torque, along with a variable Frequency drive. Then the speed could be controlled with a foot pedal.
Or looking on line a brand new potters wheel cost about $1000.00
The transmisssion wouldn’t have the stress turning a potter’s wheel that it would have moving the car, so the lubrication wouldn’t be as critical. IF this is a person’s hobby, I doubt that the transmission will rack up an equivalent of 100,000 miles very quickly just turning the potter’s wheel.