The cancellation policy says "cancelling" is not allowed - it doesn't say changing is not allowed.
This is what I would do:
Call the hotel again and politely ask them to change the dates on the reward reservation. You can either pick dates and go to the hotel at some other date.
Or try to cancel the reservation after the date has been changed since the cancellation policy might change as well for the new date.
This trick sometimes works with advance purchase reservation - and after all, there is nothing much to lose.