FFD is wrong tool for this, and model is not suitable for deformation yet due to uneven segments. You need even, regular segments, and then you can just use soft selection to make a nice easy dip in the chair. I notice also the fabric doesn't have any physical thickness, which it will need in order to look realistic.
Here is the sort of segmentation you need in the base mesh. Also don't forget the control loops that stop the corners collapsing under SDS.
Once the segments are even, just turn on soft selection, choose Dome mode, adjust the radius as shown and use the move tool to add art directed unevenness to the chair seat.
CBR