I find it easier to remove the engine separate from the transmission not all together.
Of course for me I use a chain hoist I don't have an engine lift or cherry picker as they call it with one of them angled chain things.
So for me it's always remove the hood, remove the starter, remove fuel lines, remove heater hoses, remove wiring, remove the fan, remove the fan shroud, possibly remove the radiator so it's not damaged, and pop up the transmission, unbolted, hook the chain hoist to the engine, undo the motor mounts, and start lifting the engine and wiggling it away from the transmission and just up up up and out.
I usually lift it up high push the truck out of the way lower the engine and bolt it up to an engine stand and cart it away.