I would try to be quite sure that there isn’t a small scrap of paper, like a corner of a page, stuck somewhere in the mechanism. What you describe is how the LaserWriters of my acquaintance, like the 4/600, are apt to behave when a little piece of torn paper gets left behind after a paper jam. At this stage, paper in the works from time to time is more or less to be expected, given the age of belts, rollers and such in the machine.
A little disassembly could be needed to get at it. Just follow the steps in the Service Manual.
I don’t think I ever disassembled the 16/640 I still have here somewhere, but I did go through a 630 Pro, a 4/600, and an 8500.