I got curious about this because my Mach 460 is like Charlie Brown's kite-eating tree too. I decided to pull it apart and have a look inside.
The 6-disc portion of the changer is completely separate from the main part of the tuner chassis. The changer is held in place with 4 T-15 Torx screws. Once these are removed, it can be tilted up in the chassis and the two cables (one ribbon cable, one 2-wire discrete) are disconnected the CD changer slides away from the tuner and front-panel part of the head unit.
Once apart I can see the CD rollers and mechanism. Pretty standard fare but one thing I noticed was a small drive-belt running basically the width of the changer at the "front" (i.e. where the CD slot is.) This belt is responsible for driving the wide CD rollers. See pic:
In mine, this belt looked very slack. If this belt is slack the rollers may not get enough torque to move the CD or they may not turn evenly, resulting in the CD becoming cocked in the mechanism.
In order to remove it, I had to remove a printed circuit board and de-solder one connection, then I could tilt a second board (the one I'm holding up in the pic) up and out of the way and remove the belt.
The belt is a square-drive with 0.047"-section width. The length looks to be in the 11.5" range. I went out to a local parts store and they only had an 11.7" belt. I suspected it wouldn't work but tried it anyway. Once installed, it seemed about as slack as the original. I think it actually needs a belt in the 11.3" range to be adequately tight on the rollers. Anyway, I re-assembled, soldered, connected etc and re-installed it. The unit took a CD fine but would not eject it. Eventually I got the "CD error" message again and now it thinks there's no CD in there. LOL.
Okay...I'm not giving up on this belt idea. I'm going to try to source an 11.3, .4 and .5 and will see if that helps.