I don't see the point in dropping the cash on a shift kit. IT makes less sense to me than tricking out a Yamahopper QT50. Eventually the price of parts and bike are going to meet or exceed a used motorcycle which is a better option if you`re that interested in going faster. In both cases you're on the wrong bike but at least with the QT50 you`re not dropping the cash into a cheap Chinese POS strapped to a bike never meant to handle such forces. That and most mopeds with similar engine sizes are one gear. A MB is at least 50 lbs. lighter than that.
My bike is a POS with problems tho and I dont want to mess with it unless I have to IE the factory part has proven so poor it fell off. You may have a well built bike that you feel deserves the upgrades.
If it's just a back sprocket with the single large middle hole welded on, you would need to drill 8 holes that would fit the spoke pattern. Then source the bolts, nuts, lockwashers, Then find something from the auto store/junk yard to re purpose as the rubber spacers or cut them then do the same for the mounting plates. Given that option, I would scrap that sprocket and get a new sprocket and clam shell assembly to save the head ache and potential part failure.
As far as the trash wheel; I pedaled my old wheel 3 spins then kick on the engine and cruise and only repeat when coming out of stop. That's first gear. Just set it to the lowest working gear and leave the chain there. Now I have a new wheel but my pedal hub is still crap and wobbles everywhere loosening when pedaled. I wouldn't worry about putting the chain back on that side if I didn't need the 1st gear and coaster brake.