The noise you're hearing may be caused by the release bearing riding lightly on the spring fingers of the clutch cover. There's going to be a bit of runout there.
Try this: Get under the car with it idling (use jackstands or a hoist ... all due care etc etc). Pull the release arm gently toward the rear of the car to try to pull the release bearing away from the spring fingers. Does the noise go away? (This may be hard if there's no play in the pedal and no "give" in the cable...)
You say there's no play in the pedal. This could be causing the release bearing to ride the spring lightly. You may need to adjust the pedal to give 1/2" of freeplay or so. The mechanism is supposed to be self-adjusting but you can help it by lifting the clutch pedal up and then releasing it. If you still have no play you may need to access the clutch quadrant under the dash and manipulate it to "unlock" it, then adjust it by lifting the pedal.