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You can always wrap a ring around the the custom made shaft to increase the diameter to 1/2", and therefore able to put a 1/2" bearing around that. It will be the same thing for the sprocket, except you will have to cut a slot on the ring to allow the key fit through. Of course the ring will have to be as wide as the bearing/sprocket.
Several way to make this ring: using a 1/2" diameter shaft (Steel or Aluminum), you drill out the center with a drill bit close to 12mm, or even just use a 3/8" drill bit, and then get the tool bit inside that hollow shaft and increase the inside diameter until the custom made shaft fit through. Or, you can just sit down with a file and the ring in front of a good movie, and file the inside until the custom-made shaft will fit inside. Then, you can just cut the ring along the side for a slot to fit the key in between, so you can still do a key way on both the shaft and sprocket.
Worse come the worst, if you don't have any machining capability, just go ahead and buy sheet metal at different thickness, and get thick enough for (1/2" - 12mm). Then just wrap around the shaft with those sheet metal and fit the sprocket/bearing around.
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