There were other USS Pandemoniums and the second ship was the first ship, they were not separate constructions, which means the second ship had all of the residual contamination on it.
Other Pandemoniums were:
Recruit – San Diego
USS Reina Mercedes – Annapolis
Illinois – At Great Lakes Naval Base
the real Illinois (BB 7) – New York Naval Reserve
All hands, November 1969. Washington, D.C.: Bureau of Naval Personnel: v. :ill. Page 64