As you purchased through a travel agent, no carrier will touch it.

Even though the departure time of the final segment has been changed, is there a reason why you do not want to be or cannot be on that flight? If so, ask to be moved back onto your original flight. If not, then figure out what it is that you want and make the specific ask of your travel agent.

You can always call BA to determine whether the flight you want has space for you and then use that with the agent.

For the benefit of others, for a simple return trip, book directly with the carrier. This would all have been worked out in a quick call had you booked with QR.