What reports? Are you claiming that the captain of the cable ship handed you his reports?
As he pointed out above, there wouldn't be any way to complete the exercise without some form of paper trail with regards to how much cable was supplied to the ship, how much they used, how much was paid for, etc.
With this paper trail, someone, somewhere knew how much cable had been laid. Agreed, these records may have disappeared, or at least be difficult to find, but ....
http://amhistory.si.edu/archives/AC0073.html#ref67(Only took five minutes to find) - engineer's reports, cash books, ledgers. There may well be details in there of how much cable was used, etc.
Unfortunately, I'm on the wrong continent to go visit and peruse these ledgers for myself; would you like to do the empirical research, if you're in the vicinity?