Hey Maurits,
Indeed it was the original Bluemusic module, with the head unit attachment, the seller did send over another one but i ended up buying the DSP converter kit and and the bluemusic with the dsp attachment, picture above from your post) (had a road trip so i really wanted to have some control over my spotify). Maybe it would have worked but other forums have mentioned something about having the Carver amplifier in 2003 models with its complications. I recently learned how to code the car and i noticed in one of the DSP modules, Head unit DSP was set to "nicht active", so possibily enabling it would have solved the issue, but then i assume that the music is then processed by the headunit and not by the separate amplifier itself.
For now the complicated solution is working flawlessly, only issue is i need to wire my mic so, im waiting on an extension cable, which means i have to route the cable from the cabin to the trunk. Not hard, just need to remove a subwoofer grille but definitely more tedious than the solution you have
on another note, If you look at the CD changer IO you see 2 ports, excluding the 3 pin power and ibus in the middle. one is the coax digital(which i sent a pic from my setup) and other is the 6 pin analogue. only one of the two have to be occupied. pre facelift (i) uses digital, post facelift (si) uses analogue. THe digital setups apparently cause complications
Cheers the the pictures and info!