Need help IDing 727's

The transmission in my car is toast, needs a rebuild. I decided to get somebody to do that during the winter.

I found a used 727 that a friend said was for a small small bock. My mechanic friend was in the process of installing it, but had issues. He thinks it's for a slant 6.

I have another 727 in the garage, but no idea what year it is either. It does have a rear (tailshaft) opening for a speedo gear.

I tried googling it but wasted my time. Can anybody help? I just wanna get the car mobile (cheaply) for the rest of the summer/fall if I can.