You cancel the original booking then place a second one direct with the hotel at cost A-(A-B)/2.
I've done this many times (not exactly the same, see below) with AirBnB and Redweek rentals -- once you get to know the property owner by staying there once or twice through Redweek they will happily agree to a better rate to deal direct.
I've done this many times (not exactly the same, see below) with AirBnB and Redweek rentals -- once you get to know the property owner by staying there once or twice through Redweek they will happily agree to a better rate to deal direct.