No reason to get excited man. I'm 6'3" too and my Steamroller is a 59cm. Lets just remember that not all frames/people are proportioned the same.

That being said I do know what you're talking about, but my solution is for you to check the rotation on your drop bars (the flats should be parallel to a couple of degrees rotated up from the ground) which could be affecting you. I also wholly endorse the Nitto Noodle bar. It sweeps out a bit at the drops and is generally my favorite handlebar ever.