I'm not sure what you mean by saying that content gets loaded to your app by the IFE. It simply streams (so you aren't actually storing it on your device). I've never tried to use my device to stream content from the aircraft's IFE server when there is already in-seat IFE provided, so now that makes me wonder - can you stream content to your own devices in the 777 and 787? If it's like the narrowbody fleet, I don't think you even need the AA app any more. You just point your browser to aa-inflight wifi landing page and access the content as if it were any other streaming service. The lack of ability to use bluetooth headphones with 777/787 IFE is a downer, but it is what it is. That's coming with the next-gen IFE that will be delivered with new 787s, and presumably long haul A321's.
This has been my experience. The widebodies must lack the on board server for streaming IFE.