Isn't the latest cancellation date explicitly stated on the booking confirmation? In my only currently open/pending reservation it states:

RATE RULES AND CANCELLATION POLICY:
• Your reservation is guaranteed for late arrival.
• Please contact us should you need to cancel your reservation.
• Cancellations are required by 4 PM on 23 Dec 2017 local hotel time.
• Cancellation penalties may apply.

So I would guess this is part of a template, that is the same for all reservations? What I am trying to say is: There should be an explicit date in your reservation confirmation and with that in hand, you should contact the hotel/hhonors.
If there is nothing like that & you have nothing in writing, I guess it would be very difficult or impossible to have them cancel the reservation, if they already refused to when you tried.

Your best shot might be to contact the HHonors rep here at FT. Although I would guess that she cant do anything if you cant prove that you made your reservation under a different cancellation policy (seems like the hotel suggests that there was a n-cancellation policy at the time of the booking. Had the same happen to me at the Hilton Opera Paris, made a booking and didnt realize at the time of the booking, that it was not cancellable. Made the reservation about 4-5 months in advance on points, only realized this a month later)