I would be cautious about that scheme of yours.
That's a Peerless Gear model 100 differential. These can be had for as low as $170 plus ship from places like this. There are several variations of the same model and I'm sure none are plug and play in moped application. Axle halves are not interchangeable as I found out trying to source a longer RH axle half. Spline ends are different, etc. Some are built to withstand greater loads than others, built tougher. Luckily I was able to return all the stuff that didn't work.
Mine came is what is called Peerless Differential Kit and came with blank axle halve ends albeit sufficient length to work with offset motor, completely disassembled, included a giant tube of differential grease, gasket material, oil seals, all hardware, and was more money.
Here I tried ordering a longer axle half from a different model which wasn't compatible.
Here's another example of a one wheel drive on my 2yo daughter's trike. That's about the only suitable application of a one wheel drive because on a large vehicle such as the microcar a single force of the driving wheel is acting off-center to the center of mass of the microcar making it always turn as it accelerates. I'm sure Stu Pivar's chose his one wheel drive design because it was low end mechanically simple like that trike of mine and cheap.