Label the new channel ‘Black’, then set your foreground colour to white and hit Delete to fill the active selection with black. Now the black is independent from the white and grey you can paint out areas using a white brush to simplify it further. Remember – you’re aiming for a hand-cut effect.
Select the grey areas from the image and fill with black in another new channel. Paint out any fine hairlines that appear and simplify as in the previous step, then label it ‘Grey’. Select the white areas and fill with black in another new channel, then generate a selection from your path, inverse and hit Opt/Alt + Delete to fill with white. Clean it up and label it ‘White’.
Add a new layer, then delete the Background layer. Generate a selection from your ‘Grey’ channel, and fill the active selection with a pale brown (R = 243; G = 165; B = 114). Use a selection from the ‘White’ channel, and fill with an off-white (R = 200; G = 240; B = 224) on a new layer. Repeat using a selection from the ‘Black’ channel, filling with black on another layer.