Sounds like the splines of the input shaft are not happy with the clutch disk. Assuming the disk/pressure plate/flywheel were assembled with some kind of line-up tool, have you tried to spin the input shaft a little bit? Can't that be done by spinning one of the rear tires with the trans in gear? Maybe you need to put the trans in neutral. Are you 100% sure the clutch will mate with the input shaft?
A trick I learned from JM35Sedan... He has some long (8") rods, same diameter and threaded the same as the trans bolts, with a screwdriver slot at the end where a bolt would have a cap. Use two of these, one at the 10 o'clock, and one at the 2 o'clock screwed into the bell housing. This puts two long pins coming out of the back of the engine as you bring the two assemblies together. These help tremendously to get the trans to engine angle in the proper line-up because they let you line up the bolt holes by putting the pins into the trans before the input shaft actually gets to the disk. Basically these long pins or rods coming out the back of the engine will line up the angles more easily than any method I've ever seen. Then when the trans goes in, screw in a couple of the other bolts, unscrew the rods.
Just spitballing.
-VeryTangled