An old thread but an excellent article thank you. Just followed your steps for my 2003 Z4 3.0i and had little difficulty so the GM5 will be posted off now to the Ebay repairer and hopefully my remote unlocking of the drivers door will be possible again.
I struggled a little bit with disengaging the larger black cable clip, until I restudied your photo more carefully and realised where the screwdriver needs to be located to ease it off, as a diagonal slide-off is not intuitive.
Update, 1 week later (Sep 2022) - the repaired gm5 module just refitted without any probs, and delighted to report the driver door remote lock/unlock issue is no more. Happy days.