BA have canceled the DOH-LHR leg of my SYD-SIN-DOH-LHR flights next month. It is BA ticketed Business/First through a corporate travel agent. The DOH-LHR was BA operated.

In BAEC it tells me "To reschedule your flight or refund your trip, please contact your travel agent". I contacted my agent and they told me my only options are SIN-LHR on BA operated. I asked to be rescheduled to one of the many QR operated DOH-LHR options. I don't want to change my SIN-DOH on QR, I prefer 2 flights with QR instead of 1 with BA. They offered me a QR operated DOH-LHR but said only Economy is possible. I look on QR's website and they have half a dozen flights with Business availability.

Is my travel agent playing games or does BA really force me to change my other flights so I fly with them? Is it because it costs BA money to put me on the QR flight?

If it is not BA's fault and my travel agent is playing games can BA or QR reschedule for me? Any tricks or information I should know before I ask?