Moving the seat back can work provided it doesn't cause you to lean forward more.
Just briefly, the "center of gravity" we're concerned with is with respect to the upper body only, and how far that is from the two points of support: the handlebars and the saddle. The closer the COG is to the handlebars, the more weight on the hands. It matters little where the feet are (just ignore all that "crouching balance" stuff).
So - you adjust reach in some fashion, and you adjust how much you lean, and that accounts for - with a scant few percent- how much weight is on the hands. But you describe the problem as hands going numb, and feeling like you're falling forward, and assume like most people that it's because of "too much" weight on the hands. I suggest looking at the problems without the assumption, because that doesn't always solve it or even help.