I'd like to suggest JAL Mileage Bank as your second frequent flyer program -- or at least to consider it. If you fly BA between the U.S. and Europe then you cannot earn AAdvantage miles on these flights anyway, so you might as well credit them to some program. (Hopefully you don't fly discount economy class, which earns only 25% mileage credit.)

The first year you'll have to accumulate 50,000 FLY ON points (JMB's EQPs) to reach JMB Sapphire level. That'll get you oneworld Sapphire level as well.

But now it gets interesting. Upon reaching JMB Sapphire you'll be invited to join JAL Global Club (JGC) in exchange for a modest deduction of miles (5,000, I think). Do it. You'll immediately get 3,000 JMB miles back when you credit your first JAL flight each year to JMB. And you can retain JGC membership quite easily by flying a relatively low number of miles or through an annual mileage deduction. But the real reason for keeping JGC membership is because, if you're a JGC member that accumulates at least 20,000 FLY ON points, you'll be given oneworld Sapphire status.

I don't know any way to keep oneworld Sapphire with just 20,000 EQPs except through JAL's JGC (excluding AA's Platinum Challenge). You'll have to do the math very carefully, but if your strategy is to get oneworld Sapphire in another program in order to get domestic U.S. lounge access, JAL might be the best way to do it, at least on an ongoing basis.