This is very interesting. I would start by asking for standard EC261 (600 EUR) from AY. Their reroute would most likely have you qualify for that.

But the PE/downgrade situation seems to be a matter outside of AY's control. They rebooked you into PE, but BA being late caused you to be re-rebooked. Was your final flight LHR-HKG operated by CX? I would probably take the downgrade stuff up with them as you had CX PE and were rerouted to CX Y. But it could very well be that all these airlines will just blame one another. One thing seems clear to me: AY will not be liable for the downgrade compensation.