If I had to replace the automatic transmission, I would also pull the engine and trans as a unit.
I replaced my engine last year and pulled both together. I used an engine hoist with a eng. tilter. had rear of car up on blocks, and the front on jack stands.
the only challenge I had was the hoist only went up so high, the engine would not quite clear the radiator support. so used my 2 hyd. jacks and raised the car to remove the jack stands. then lowered the car down and everything cleared and rolled the hoist back from the car.
those damn little casters on the eng. hoist do not want to roll on rough asphalt with the weight of the eng. on them. I had 2 long pieces of flat steel about 10 ft long I slid under the front of the car to roll the hoist on. smooth as butter then.
that automatic is one heavy sucker, and I don`t have a trans jack, and also would have had to jack the car up higher to get clearance to be able to roll the trans out.
replacing a 4 spd manual, piece of cake leaving the eng. in. can do it one handed.
a gantry crain with a chain hoist is the ideal way to do it. Harbor freight has one for $600.00.
a nice warm shop with a lift would be ideal too
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thats my 2¢ worth.
Charlie