Yes, the furring strip is sitting exactly where the bottom of the crown would hit. My chair rail and base molding will be the same as in the playroom. Not sure about the chair whether two strips are necessary since it's about average size, but the base is pretty thick.
I'll throw out an idea that the GC threw out. For the chair rail since my riser is SO high, would it make sense to have the the chair rail slant upwards by the stair and then go a bit higher on the riser. I opted to keep it simple since I thought visually it might look odd for the chair not to continue at the same height. Any thoughts on the issue?