If I understand the situation correctly the washer is free to move so does not stay alinged when you turn the clutch on its side to fit it. I presume we are talking about a Briggs and Stratton unit here?
My solution to this would be to turn the clutch over so that you can see into the threaded hole, line up the washer using a round object then squeeze the rotating section of the clutch hard against the threaded portion with your hand. Hopefully this will keep the thrust washer in place while you feed the unit over the crankshaft extention. The clutch should then be easily screwed into place.