Yes, Disney Signature Services (DSS) is separate from customer service, reservation agents, guest relations, etc. More info can be found here:
https://disneyworld.disney.go.com/en_CA/guest-services/signature-services/
DSS is basically a "concierge" type group that offers planning assistance in advance of your trip. Booking a CL resort room or suite gives one access to DSS. DSS is the group that handles the Extra FP program.
You can try calling them and asking about your trip, but I suspect they are going to say "the program has been very popular and we hope that it continues, but check back closer your dates...."
You can't book this program until 90 days from your
check-out anyway, so you're really not missing anything at the moment. You have plenty of time to plan how to use 6 FPs each day.
Hope that helps!