The drawing calls out an 11hp for 536.886220.
1. The clutch moves the lever assembly that fits over the trunnion bearing.
2. The trunnion bearing has a hex shaft going through it. One end of the hex shaft has the friction disk drive plate. The other end has the big drive pulley.
The clutch lever should move the lever assembly, trunion bearing, hex shaft, drive plate and drive pulley at the same time. So it looks like the drive pulley can have some swing but minimal i.e. not enough to have a line up problem you mentioned.
Suspect, most likely to least likely:
1. The trunnion bearing is off the U's of the lever assembly.
2. The screws of the arm extending from the lever assembly are out or loose causing the clutch lever to have zero or minimal effect on the lever assembly.
3. The screw holding on the drive pulley has fallen out or overly loose.
4. The allen screws holding the drive plate to the hex shaft are loose/missing.
5. Your cable adjust is stretched too much to pull in the lever assembly.
6. The drive pulley key is broken.
7. Give what you have said slop in the friction disk hex shaft (two in this system) is not happening. Slop is only in the drive plate so no issue with the friction disk or its carrier.
