The fix that I described in my post above, dated 10/14/18 is still working perfectly after 2-1/2 years. Our Kenmore , purchased 18 years ago in 2003, is still purring like a kitten, just like it did when it was new. It made a loud rapping sound during spin cycles for 10 years before I figured out how to fix it, so no permanent damage was done.
Note that I also separately “leveled” my machine, but that term is a gross misnomer, at best. What is really important is making sure that all four legs are pressing on the ground with about the same force. I call that “balancing” the machine. Here’s how to do that, with the machine not running:
(1) Stand in front of the machine and try to rock it back and forth by pushing it '''''digonally''''', say from the left front leg towards the back left leg. Note the amount of rocking you get.
(2) Perform the same test on the other '''''diagonal''''' direction. If there’s more rocking in this direction, lengthen the front left leg adjustment a turn or so. If there’s more rocking in Step(1) lenghten the right front leg.
(3) Repeat Steps (1) and (2) until the machine rocks equally no matter which diagonal direction is pushed. Done!
(4) Now run a spin cycle, and the machine should be much more stable.
Note that I did not place a level on the machine to make sure it was “level”. If it looks grossly tilted you can correct that if you want, but be sure to run Steps () to (4) afterwards. That’s the key to a smooth running machine. Note that floors, themselves are not always flat. If the machine walks a bit to a new location, you may have to repeat the balancing process.