Apparently, you can use the FSA alone to obtain a unique hash code for each item:
This is not necessary at all, since an acyclic finite state automaton can be used as a perfect hash function. If you sum the right language cardinalities of the transitions followed, you get a unique hash code (1..n, where n is the number of strings in the automaton). For efficiency, you can precompute the cardinalities in the transitions or states. You can then use a normal array for whatever data you want to associate with a word.