For an aluminum adjustable ball mount that fits all of the criteria you mentioned you would want the part # DTSTBM6800-2S. This has both ball sizes you need, can drop down as low as you need, and has an anti-rattle device built into the ball mount as well. view full answer...
The Curt hitch part # C12068 that you referenced has a trailer towing capacity of 3,500 lbs so it would easily handle a small trailer that has a 700 lb motorcycle loaded in it.
For trailer wiring you'd then want the part # C59236 which is a confirmed fit. For a ball mount part # C45522, 2 inch ball part # C40018, or 1-7/8 inch ball # C40001.
Be sure to check the owners manual of your vehicle for the towing capacity as well. view full answer...