Im 90% sure the noise is the top sprocket slipping on the top output shaft, just from pictures of the wear.
It kinda looks male and female both have wear, so maybe? Just a tighter female (lot cheaper/easier), would fit snug for another couple decades on the worn male shaft.
Failing that, tack welds, or a soft metal, like copper, couple thin strips, and press (hammer) the sprocket back, and the copper engraves both splines and removes any slop