It's a floating two terminal circuit, so either terminal can be considered "ground" or common,
and have the woofer and input directly connected together at that node.
and have the woofer and input directly connected together at that node.
You can. You could also turn the circuit upside down to look more conventional. What is important is that you keep the amplifier and speaker the same polarity as each other.do I connect the negative terminal before the 2 coils like this?