Maybe rig up a bolt to pass thru the bushing while pressing to hopefully keep it from popping out to the side? I'm thinking a bolt thru a flat plate to keep it aligned with the press axis. Effectively making it act like the pin on your press could pass thru the bushing.
Do you have the self test kiosks in Colorado? If so, use one of them so you can fiddle with the connection yourself. And get yourself a cheap OBD reader so you can experiment at home with the connector to see how reliable it is or to determine if you fixed it.