How about a recursive solution where you stop when you can no longer apply the remaining alphabet to the search space? That way you don't try all combinations, but only those that have a potential of succeeding.

# pseudocode
sub find_some ( @choices, @alphabet ) {
    $results = [];
    for $choice ( @choices ) {
        if ( choice_is_in_alphabet ) {
            @new_choices  = @choices  - $choice;
            @new_alphabet = @alphabet - letters_in( $choice );
            push @$results, [ $choice, find_some( @new_choices, @new_a
+lphabet ) ];
        }
    }
    return $results;
}
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You will be left with a spanning tree of all good solutions. With a stack you could also remove the recursion.

Update: Scope error

Update 2: I have noticed a couple of minor logic errors as well, but they appear to be easy enough to correct.