HillRider - I think it's a Shimano HyperGlide Freewheel. From SB's pages:

http://www.sheldonbrown.com/free-k7.html

If you look at the pictures under "Identification: Freewheel or Casette" it looks just like the second picture from the left. I realize now that there was no reason for me to remove the retaining ring that holds the cogs on. The retaining ring itself was tight, with no play in the cogs.

What seemed loose was the nut deep inside - one side of which is basically a bearing race.

Homebrew has a point regarding the crank. Just because it doesn't make the noise when there is no load on it doesn't really eliminate the possibility that the problem is there.

JDT - doesn't seem like the pedals.