I had a similar occurrence on my 69 340 four speed. In my case the clutch fork pivot had failed. It is held on by two bolts and is easy to replace AFTER you pull the trans. Good luck and let me know you find when you teat it apart.
I think I may see it now. There is a broken ring hanging loose on the throw-out bearing assembly. I think maybe the bearing is only partially moving. It appears to be a two part bearing maybe? It looks to have an inner and outer cylinder. The clutch is a diaphragm type, but the built 360 needs a stronger clutch anyway. But it will be a bear to get out.
