Have the same issue; reduce chatter somewhat but still an issue. Please explain balancing process.
Most any machine shop can do this. Take the flywheel and Pressure plate with the mounting bolts to a machine shop. They will mount them together or you can do it. They will put the unit on a machine and spin them up (similar to balancing a tire) and add or remove weight where necessary. When balance is achieved they then mark the flywheel and pressure plate so that when you reassemble them on the car they will be in the same position to each other. The clutch disc is not involved in the balancing.
If the chatter is at low rpm's (600-900 rpm) the clutch/flywheel balance is most likely not your problem. The imbalance would show up more and more as you increased engine speed. Check your motor mounts again, u-joints and rear end pinion slop. If you have a lot of looseness in the rear pinion mesh it is likely to cause clutch chatter. Also check for loose motor to bell housing bolts and transmission to bell housing bolts. Another possibility is bad rear spring rubber bushings or loose u-bolts. One final problem could be improper clutch finger adjustments. To check this, put the vehicle in neutral, set the hand brake, chock the wheels to prevent rolling, start the engine and let it run at idle. Slowly depress the clutch pedal and note if there is a pulsation in the pedal. If there is a noticeable pedal pulsation, the clutch pressure plate needs replacement or adjustment. This last test eliminates motor mounts, u-joints, rear pinion, rear spring bushings, loose rear spring u-bolts and flywheel/clutch pressure plate/clutch disk balance problems.
The chatter occurs when starting off. forward or reverse. The "vibration" is when the clutch pedal is released and the car starts to move. When running, it's smooth; "vibration", not severe, is when the clutch pedal is being released.
If you do not have any oil or grease contamination of the clutch disk, you have bad or mis-adjusted clutch plate fingers. This will require replacement of the clutch plate. Balance (vibration)problems of any component of the clutch system will remain noticeable even after the clutch is fully engaged and is not the probable cause of the clutch chatter. If you notice vibration in the clutch pedal as you slowly depress the pedal in neutral, it is most certainly the clutch plate.