As for KE... TA/Corp are one in the same, the TA is a subsidiary of us. They get a "discount" flying Delta, which ticketing usually is the same price as any travel website, so I assume it reality it's some sort of "spiff" on the back-end for the TA or something, unless Delta is cutting a rebate check at the end of the month.
If I were in your shoes, I'd press them on this. They are effectively telling you that x hours of your time (not to mention the hassle of connecting in Shanghai or racing around HK) is not worth the fare difference between DL and KE (assuming KE costs more).