It appears (not yet verified) that one or more of the (plastic)
rollers under the refrigerator may have disintegrated (or, be
in the process of doing so).

[I suspect the "webbing" inside the roller has fractured based
on the bits of plastic I've discovered under the unit]

I'm thinking of strapping it to my "refrigerator dolly"
http://www.aaarentalsredwoodcity.com/itemimages/3058.jpg
and leaning it back "for transport" to expose the underside.
By carefully choosing the side from which to approach the
refrigerator, I should be able to MOST elevate the rollers
in question. Not the greatest in terms of accessibility but
should be enough to expose the rollers and any mounting hardware
necessary to remove/replace.

I can't imagine any OTHER way to get at the underside of
the unit? And, I'm sure we're not the only ones who will
have had to replace these rollers (given that they are a
replaceable "spare"!)

[Note to self: remove liquids from refrigerator before doing so]