Moosh,
Make sure that the clutch release arm is not holding the clutch partially released, do not base an assumption solely on a slack cable. If the flywheel has been lapped too far into the crankshaft taper, a thicker than normal thrust washer fitted, or the ring that the clutch cam release sits on has been reposition on the crankcase spigot; any or all of these may cause the clutch cam to be bottomed out. You should be able to grab the end of the clutch cam release arm and rattle it about slightly. This can be a bit tricky on an T/S6 model, due to the routing of the clutch cable and the primary chain guard.
Yes there are (or should be) cork inserts fitted to the flywheel disk. These can be worn, but that should not normally have a dramatic effect on the clutch action.
Probably the second thing to check is the springs, all present and of the correct length and rate.
There could be problems with the carrier sleeve fir on the flywheel hub and the bearing bore in the sprocket, but these usually manifest themselves as problems with the clutch dragging (excess clearance allows the clutch plate to tip and rub.)
Also any oil and grease from the bearing that has found its way out on to the corks (or alternately Ferodo) will inhibit grip. Normally the grease is directed away by a slinger, but over zealous application of the grease gun could have overwhelmed it.
-Doug