Heres how I do it. Remove the front bumper, radiator support all that. So its wide open. Pick the engine weight up with a crane. Un bolt the engine mount to subframe, and trans mounts to subframe. Remove the bolts holding the subframe, let it hang down. Then just pull it all out. Its just so not worth the struggle of trying to leave the transmission. Its so nice to just pull it out, unbolt the trans, pull it off, do what you gotta do, mate them together and install. You can unplug the ECU and all the colored plugs and drag the entire wire harness out with it. Makes install much easier.
2001 Audi S4 2.7T
2002 Audi A6 Quatto 3.0