I've swapped several engines and tranny's over the years, and I can't remember ever doing both together. I've pulled a few engines with the trans attached when junking the body but can't remember the last one I put in as a motor/trans combo. Even when putting both in, I've usually put in the engine and then put the trans in seperate.otherwise the trans stays put when I swap an engine. Even with a cherry picker.
Many, over the years, I've done with an a frame and a chain fall, having to push the car out from between the a- frame, and back under and back a pickup truck between the rails to set the old engine into, and to pick up the replacement from, then push the car recieving the transplant back between the rails. What is available for the job definitely dictates how that job gets done.