Thanks for the reply.
The reference is in Volume 23 of the ORN, page 204.
Although it is in the ORN, it is not an official report, but is an extract of a newspaper article, the July 2, 1862 edition of the Mobile Daily Tribune. The source of the information in the article is said to be "a young officer of the Navy, who participated in the battle of White River".
Most of the information in the article seems to be correct, but still newspaper account are very prone to errors and misunderstandings, if not the occasional outright intentional distortion of facts, so, without a verifiable source I don't know whether to believe the Fort Randolph connection or not.