Your pic suggested the "pink" is insulation. If it is then I have a solution. You will need a real box for a fan. You could sister a 2x4 onto the 3/4" furring that is already in the ceiling by pushing the 2x4 above it -- yes, this will compress the insulation. Fasten the 2x4 by shooting screws (2 1/2" or 3") through the ceiling drywall, the 3/4" furring and the 2x4. The two pieces of 2x4 should be at least 12"-14" long.
Now, you have a solid edge where you can screw the fan box with screws through the sides. Obviously, you need to fish the wires through the boc and make sure you have a wire connector that prevents sharp metal from cutting into the wires.
Follow the fan's installation directions as to wiring and mounting. Since the ceiling is slanted, you will need to let the mast hang freely to orient the fan properly.
Someone else might have another idea . . . This is what popped int my mind.