Matt, there are no adjustments for aligning the clutch pressure plate cover to the flywheel. It either fits of it don't. Apparently, your flywheel is running true so the discrepancy must be that the clutch cover is bent. The bearing sleeve part of the cover MUST run true, otherwise there will be mucho vibration. Mount the bearing sleeve in a lathe, rotate, and notice the runout on the cover plate.
I'm not sure what you mean by there being no "pilot shaft". The clutch friction disc is riveted to an "output shaft" which runs in the bearing sleeve. The throwout bearing rides on this bearing sleeve to operate the three clutch release fingers.
I think I may have found the problem. After closer inspection I noticed a bur on the pressure plate where it seats into the flywheel. After filing it off and reinstalling the clutch the vibration is almost gone. My comment on the pilot shaft came from one service bulletin I found but it is talking about the model 65 and 75.