On ba.com, I can only find availability MAD-EZE on the 18th Oct, and I can get a J-J connection that day.

So it may be that Expertflyer is inaccurae, or is looking at IB's system which may have different availability than BA are able to access.

ORY-JFK-EZE might be a possibility,maybe using OpenSkies to JFK (if that counts as ba rather than as a second partner which would increase the miles), but that'll need a call to ba as it's not coming up online. And unless you want to visit NYC I think I'd stick to the IB routing.

I suppose you could try going -LHR-"USA"-EZE on ba and then AA/LA, with the "USA" options being JFK, DFW, MIA or (outside the box, via LGW) Punta Cana.

edit: if this is a flexible trip, IB have some alternative availability to COR or MVD, a train/boat ride away.