Since AA doesn't fly SFO-LHR (only BA, albeit carrying AA codes) and since the BA nonstop does indeed arrive after LHR-VCE has departed, I'm presuming that the AA segments involve a US connection, arriving at LHR early enough to make the VCE flight. Otherwise the move to Gatwick is a giant pain.

On the other hand, the IB LAX-MAD nonstop (which also carries AA codes) does indeed allow for a direct connection through MAD with a sub-2 hour layover, so that would be the fastest; DFW-MAD on AA would also allow a 3-hr connection through to VCE.

I personally have found that connecting through Madrid is quite painless; since you would be entering Schengen there you'd have to go from T4S to T4, but that's no big deal. It certainly beats the bejeezus out of having to do the LGW schlep if that was the other option.