Clutch Help/Guidance

[Tak28Tudor]

I need some folks with experience/expertise to help guide me: I have had my 1928 Tudor for approx. 2 years. The car is an older restoration (70s or 80s) but in overall good shape. I have attached a picture for reference.

The next project is to address the Clutch Chatter. The Clutch makes Chatter noise and vibration when releasing the clutch in 1st Gear and in Reverse. (Makes a knocking noise and shakes the entire car.) This only occurs when releasing the clutch in 1st Gear and Reverse. Does not occur at an other time. Transmission shifts fine and is smooth. The car does likely have a rear main leak....but it's not bad (a few drops of oil after sitting.) I was told to try and "Burn" the clutch dry as it likely has oil on it or use the vehicle more and it will likely work itself out. No dice. I still have Clutch chatter as mentioned above. I am determined to fix the issue as the car drives so nice. In your experience, should I pull the transmission and just replace clutch, pilot bearing, throw out bearing? What about the the throw out bearing hub? What else? I have never pulled the rearend/transmission before and I only want to do this Job once. Any guidance would be much appreciated. Thanks!