The GM3 module for 04=06 model / year e53 slightly different. They have circuit for soft-close actuator installed on 04-06 e53. The best bet is to try to code new GM3 module using coding software like "NCSExpert". Also, GM3 module controls "Servotronic" steering on 4.6is. Steering will be very tight if servotronic option not enabled in GM3. You will have better chance to resolve issue if you get GM3 module from 02-03 e53.

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2012 X5 x35i My new toy
2005 X5 4.4 Her's (Retrofitted Servotronic Steering Rack)
2003 X5 3.0 Mine (Retrofitted Servotronic Steering Rack and Heated Steering Wheel)
2001 M5 Son's car
2000 540i 6sp Sports pkg, supercharged. Son's car (Sold)
2001 530i (Sold)
1999 528i (Sold)
1975 2002 (Sold)