With the shim in place, did you try whacking the clutch while the AC is on and engine running? If it grabs, you've still got a clearance problem. It sounds like the clutch might be toast though. You can replace the clutch without emptying the system though, so I would try that first. Incidentally, while it was running all the time was it cooling? If not then you might have a compressor issue as well. Also remember that if the system is in auto or defrost mode the compressor may run with regardless of whether or not the AC button is toggled on or off.
2004 Imola BMW ZHP
2006 Commander Limited Hemi QD2
"Bought, Not Built"