According to the UC application guide on High Unit transfers, the maximum transfer units for UCLA is 86.5 semester units/130 quarter units and they do not accept High unit Juniors or Seniors.
82 UC transferable units puts you in the High Unit Junior category.
You stated that you have verified with UCLA that you are eligible? You have this in writing? AP/IB credit is not included in the maximum unit count.
https://admission.universityofcalifornia.edu/counselors/files/quick-reference.pdf#page=34