AA is responsible for the bags.

It has nothing to do with southwest.

You spoke to a front line idiot at AA baggage that wanted to just weasel out of the issue. Call again; do things in writing; ask for supervisors.

(Note- OP tried to get the bag in DFW, and AA refused to give it to him. They kept it and delivered it to SFO. OP also cancelled the DFW-SFO flight...all this in his post)

The problem of course is how to gain leverage. Send AA a demand via fax; threaten to pay for it and file a claim...then pay for delivery (Uber?) then file a claim w AA. Small claims or credit card claim (assuming the ticket was on a credit card) if they refuse