https://saleslink.aa.com/en-US/resou...le-change.html

This is a good source of information over your options. Your post is also a timely reminder to everyone taking ex EU's that policies aren't equal amongst Oneworld carriers. AA is obliged to fly you from CPH to your destination and that's what they'll be looking to achieve. They have a similar rebooking policy in the sense you can request an alternative starting point within 300 miles of CPH but London is more than 300 miles away. I suspect a rebook to a new date/time of your choice within 14 days is going to be your best bet (lowest fare bucket in same cabin in flying Business) and to similarly request the same to coincide with your separate positioning flight with BA