If you want to know how we used to do it, this was the old muscle way. You put your legs folded under you on the seat and grab the gearshift stick, still in the trans, pickup on it and slide the trans. back and let down to the floor, all at the same time, using only the gearstick. It's amazing how tough that little piece of tin is, that holds the stick in. You can take the gear stick out, then and slide the trans. from under the truck. Installing it helps, if you have an extra man, to push the trans. forward after you get it lined up at the clutch. I probably couldn't do it this way now, but I have done dozens of them like this, when I was younger and dumber. I always knocked the PTO shaft off and left the gear bolted, to the trans.
Your way with the jack is the best way to save your back for another day. Great pictures!