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Never mind, I just noticed that I can't use AA miles for transAtlantic travel on BA at all.

Not necessarly true.

You can use AA miles on BA flights to UK from Canada, Mexico, and Caribbean. Since you want an award ticket, your connecting flight to one of the locations listed above would also be included.
If you said, "oh never mind, I just found out I can't use AA miles on BA non-stop between ORD-LHR", then you would be correct, but if you are willing to do ORD-YYZ(AA)-LHR(BA) then it's possible.

Also AA & BA is allowed to codeshare on few flights between US and MAN. BA has JFK-MAN which allows AA to codeshare. You are allowed to use AA miles on that route. You will also earn AA miles according to AA rules if you purchase AA coded flight.

Thanks for the additional info. If this were for myself, I would go through an extra stop - or just make it easy on myself and fly AA. But I am trying to gift the award to my parents who will only fly BA - so if they are picky enough to only fly AA, then they are certainly not going to make extra stops in Canada or Manchester. So it looks like they're paying cash for their tix. But thank you for correcting my overly broad statement.