Yep ba.com does support KA. The initial hit says no availability, do you want to include partners, and the only partner listed is Dragon Air
In terms of talking to the EXP agent, ask them to ask revenue management to clear it with CX. For sure they will know who to call. I can understand the EXP agent themselves not knowing who to call, but RM should.
I am still inclined that KVS is right, though surprised ba.com is wrong. I have found it to be pretty accurate in the past (that's why I asked is kvs still showing availability?)