The 1.76 input shaft is supposed to be 12 7/8" and the 1.82 input shaft is 12 5/8". So, it sounds like they sent you the correct one for the 1.76. If you truly need the 12 5/8" long shaft, you can not use the 12 7/8" as the torque convertor would not be able to slide on far enough. The gold wedding band fits inside the small slinger/shield that rests against the hub inside the high gear drum.
Bill M