I'm with Botto for Core strength. Do some upper back exercises. A good guide someone told me once was that you should be able to lift your hands just slightly off the bar without feeling a strain on your back, or you're putting too much pressure on your hands.

The elbow locking issue usually causes a sore back and neck as opposed to numb hands, but it wouldn't hurt to take note of it anyway.

And finally, moving the seat back MIGHT actually be a good idea. Getting a good balance over the cranks is part of a good bike fit. roadwarrior is right that saddle position isn't to adjust cockpit length, but deepakrvao was suggesting it for balance over the cranks, which is exactly what it is adjusted for. Peter White has a great explanation of this on his site.
http://www.peterwhitecycles.com/fitting.htm