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How loose are the handles on there pivots, I have seen handles lose their leverage because of binding or they are very sloppy.
The problem is in the handles or the lach mechanisms, pull the door pads and remove the parts clean inspect and lube, reinstall and adjust.
trying to do this from outside the door just will not be thuro enough, old grease and oil gets very stiff along with atracting dirt.
Beautiful car, the 71 and 2 RR are my favorites.
Good luck