You won't be able to earn on your BA flights between the US and UK if you credit to AA unless you actually fly AA. Also, you wouldn't get any status bonus on BA flights by crediting to the AA program.

Having said that, on QF you might struggle to maintain status now they are enforcing the 4 segments on QF or JQ.

Alternatively, you could look at an AA challenge to fast track to status and use it for lounge access and credit to AA or QF when AA isn't possible.