In order to get upgraded to a signature suite, you must book a king bed room with a harbor view (Premier King Harbor View), which is like $50-$70 more per night than the cheapest room (Premier King) so that you can get $500 more value to be upgraded to a signature suite since that is the next 1 level upgrade. It is the same exact room but with a harbor view. To be more specific, if you book the cheapest room (Premier King), you will only be upgraded to the same room (Premier King) but with a harbor view which is not really an upgrade. The hotel changed their policy and now is only offering a 1 level upgrade.
The prior reviews from other AMEX FHR customers say that if you book the cheapest room (Premier King), you will get upgraded to a Signature Suite.