Normally you can pull it up and out if you release the clips that hold it in on each side. You will have to move the shifter all the way down to the lowest gear selection, and that should give you enough room to pull it forward and tilt up and out. Its kinda tight, so be patient and careful. If you cant pull it far enough out to touch the shifter, (even in the lowest position) something else is holding it, like a clip or something.

Im not sure how your alpine kit is for holding your radio in, but I have an aftermarket radio in my 90 740 and I can still get it out. I guess I cant remember what it was like with the factory radio in there, but I dont think the adapter kit that is holding my radio is in the way anymore then the factory radio was.

By the way, I am trying to trace down the same problem. Let me know what you find out, and I will let you know if I get anywhere on the problem too. I have had my fuse box out and flipped over, but didnt see any problem areas.