Remove the upper floorboard and take off the angled clutch inspection plate on the bellhousing. Take a flashlight and examine the hub of the clutch disc. If there are no springs around its circumference, that's probably why the clutch chatters. I have never had any luck with springless clutch disks in 50 years of playing around with Model A's. They were an aftermarket item marketed for heavy-duty applications, such as hard-working trucks. The springs are there for a reason = to counter fluttering when the clutch pedal is released. Without them, what you feel through the clutch pedal is the disk gyrating.
Other causes may be contributing to the chatter, as previous posters have suggested. But the reason the car has probably sat unused for 45 years is because the clutch chatter was too much for a previous owner or owners. Consider the other suggestions offered so far, but if there are no springs in the clutch disk hub, you're wasting your time applying Band-Aids. If you do need to replace the disk with one containing hub springs, follow "larrys40" recommendations. There will be no better time to upgrade and refurbish these important items than when you are changing the clutch. Or do you want to go through all that hassle again just to change a worn-out throwout bearing? Me thinks not.
But, first things first: are there springs in the clutch disk hub?
Marshall