I don't see the confusion.

The reference to Thompson simply means that Basil Lubbock's book on whaling mentions Thompson as commander of the Diamond in 1819. Since that was the year the ship was lost, it makes sense that that would be the voyage Lubbock mentions.

There's no necessary contradiction between Aberdeen as home port and the "Peterhead" of the song. Perhaps the ship called in at Peterhead - about 25 miles northeast - and that visit (or those earlier visits) prompted the lyrics. In any case, the songwriter would not necessarily have known - or cared - that the Diamond belonged not to Peterhead but to Aberdeen.

Just guesses.