Hashing of "switch/case" selections

[Robert Dewar]

unique hashes are not even desirable, note that in particular the
original input meets the definition of a unique hash. I don't find
the concept at all useful in this context.

What you are loking for is of course a near-minimal perfect hash, that
is what BCPL compilers used for case statements. Quite a bit was published
in the BCPL context about this approach, so I recommend looking into the
literature (it is quite old, you might have to go to a library - GASP :-)