AA in theory can contact their oneworld liaison focal point who may be able to liaise with BA to move the flights. The alternative is to try again when you are within 24 hours of the flight, since on paper BA then have control of your ticket. However my suspicion is they may still ask you to contact AA about this. Finally you could try at the airport to see if they will move you to the next day. Having said that, the customer guidelines have only just come out, it may be AA will be more helpful after they have seen/circulated the guidelines.

You won't get any tax refund, since you are still in business class, for which there is a higher APD, and there's not much BA can do about that. In any event you are flying to the UK so there is no APD. However in other cases BA have given £150 on a cash card for this sort of change - admittedly that tends to happen for last minute changes. So if you continue with your schedule then you could ask about that. The alternative would be to request AA to put you all in EuroTraveller / World Traveller, if only to save the miles concerned, again assuming there is availability for this.

The reason for this is a shortage of flight crew. This was an A350 too...