As this topic remains up way past its bedtime, here's my $.02 worth:
Amos makes it fairly clear,

"Subject: RE: Where are 'The Two Sinkers/Sunkers'
From: Amos - PM
Date: 24 Dec 07 - 10:54 AM

While striking bottom is done by heaving the lead, it usually has only one sinker on the line, a tapered thing like a sash-weight, with a hollow cup indented on the bottom for the wax plug used to collect bottom sample. I have never seen or heard of a two-lead method, and I think this is an invention born of misunderstanding.

Sinkers, or sunkers, are submerged rocks, so named because they have a nasty habit of sunkin' yer boot when you least expect it."

      -except that it is usually called "sounding", not "striking bottom".

STRIKE, to, the act of lowering the colours of a warship in battle as an indication of surrender.
A vessel also strikes soundings when she can reach the bottom with a deep-sea lead when coming in from sea. This is today generally accepted as the 100 fathom contour, and a ship is in soundings when she is inside this line.
    -The Oxford Companion To Ships And The Sea.

Striking soundings (at 600ft.) is not at all the same as striking bottom, except perhaps in the minds of landlubbers in "an invention born of misunderstanding" as Amos says.
This is a common enough phenomenon, as Rod Stradling shows in his magazine Musical Traditions:
http://www.mustrad.org.uk/mondegre.htm

It would not surprise me if a singer changed "see bottom" to "sight bottom", and another heard it as "strike bottom". As a sailor, "striking bottom" is the last thing I want to think about.

Edith Fowke printed Clara O'Driscoll's (1899-1978) version for The Penguin Book of Canadian Folk Songs. I don't know if we have a higher authority.

We'll rant and we'll roar like true Newfoundlanders,
We'll rant and we'll roar on deck and below;
Until we see bottom inside of two sunkers,
Then straight through the channel to Toslow we'll go.