This is going to be a difficult one, American didn't cancel your flight, BA did. You are very unlikely to get AA to refund much of anything on this one. You had the right to cancel the return completely at this point or request a schedule change that worked for you personally.Stop using words that are emotional such as demanded or extorted, they only make the other side defensive and less likely to help.
Send a summary to both AA and BA of the facts of the case and what you think is an acceptable customer service gesture.
I did not receive notice of the involuntary schedule change, BA cancelled the flight on 12/13 resulting in an unplanned 24 hours in London resulting in an unplanned hotel stay that cost XXX.
There was a mix up with the re-issue of the ticket due to the involuntary schedule change, as a result I was only presented with the option to pay an additional 22K miles which resulted in an unplanned transfer from my wife's account costing $232 and 22K miles we had not planned on using. Additionally, this resulted in having to pay the UK Air Passenger Duty of £172 X 2 passengers which cost $493 when converted to USD.
While I understand that travel often has unplanned changes, this involuntary change resulted in significant unexpected expenses. As a result, I am requesting a customer service gesture of XXX to offset these additional unplanned expenses.