Lew wrote: "There's no rule that will
infallibly tell you which of the four is "the" radical to look up the
character under. I haven't seen a dictionary that lists characters
under *all* their radicals. Does anyone know if such a beast exists?"

You have pinpointed one of the biggest pains in the ass associated with
learning Chinese. Actually every character has only one radical. The
more you use a dictionary, the more luck you'll have figuring out which
of the possible radicals is *the* radical. One small hint is that it
is usually the outermost.

Some dictionaries - usually the bigger and more scholarly ones - have a
section after the radical index entitled "hard to find characters".
Those sections can be really useful, as the authors have often done a
very good job of anticipating which characters are likely to confuse a
learner.