Jim, the transcription that appears at the website is clearly erroneous in some places, as you've undoubtedly noticed.

The "mountain" stanza sounds like this to me:

Henry tol' the Captain, mountain's fallin' in
No, Captain, yous a bad mistake
Hear my hammer handle ringin' in the wind
Hear my hammer handle ringin' in the wind, God knows
Hammer handle ringin' in the wind


"Yous" doesn't make much sense to me here, unless, as you suggest, "made" has been elided.

I don't hear "that's" anywhere in these lines.