Everytime I redeem for CX from AS, I also receive the AS/QX segment to CX's gateway city. The terms mention the nearest city, so for me in SEA it would be YVR. I have had no problem flying to SFO, and sometimes even to LAX (due to availability and timing preference) to transfer to CX.

I am not sure being in the midwest and requiring a connection to the gateway will make a difference. I don't think so, and I would call again and talk to a different agent.