You should be able to remove the engine w/o opening the air con. Unbolt the compressor from the motor and put it to the side. I've never come across a motor that needed the aircon opened to remove it.
If you can just take the gearbox out, it's easier in some ways, but yes, you'll have to lie on your back and you need 2 people to drop the box out. However, there's significantly less stuff to disconnect to get a gearbox out. The spigot bearing may require you to take the flywheel off too depending on the design. Be prepared to hurt yourself trying to undo the flywheel bolts