I think I'm getting closer (at least) to understanding this.  Instead
of:

$serverVariable["server"] = 1

....what I want is, in reality:

lvalue_of_what_is_pointed_to_by($serverVariable["server"]) = 1

....that is, this $serverVariable["server"] contains a TkVariable, and
after the assignment it contains a 1 instead.  I want to set not the
array value, but the contents of the array value.  A reference, if you
will.

But how?  I'm still trying...