Speedometer stoped working

[70SS454]

My speedometer recently quit working. I have a 1970 chevelle ss with a Muncie 22 4 speed. I have a new speedo cable that does turn the speedometer (I tested it with a drill attached to the cable on the transmission end). The red drive gear also looks fine. However the worm gear in the transmission looks to have broken off. I have attached a picture of the plastic gear on a metal shaft inside the transmission that I took through the hole for the drive gear. Is it broken and can it be replaced without pulling the transmission and breaking it open? Maybe by a transmission shop?