JPM has been around a long ass time, I believe him...
if you want to "hit the outer head" of the bicep, you have to hit the bicep (obvious I know).
Don't waste time on close grip bullshit, you'll hurt your elbows or wrists.
Don't use an EZ curl bar (why do you want to do anything easy in the gym?)
You may have to drop some lb's to get there but what you have to do is actually turn your palms so that they are facing up and parallel to the ground (use a straight bar). Start light because of the stress on your elbows, but your bi's are fully flexed when your hands are in this position.
and... genetics are a bitch