My experience is that reach is independent of seat position. What I didn't say in my previous post is that I could keep myself from sliding forward by moving the seat forward, but I still ended up with perineal numbness when riding.
I eventually bought a Selle SMP TRK. With this saddle, I've ridden 46 miles without numbness (hey, I'm 73 and lucky I can ride 10). If I move my seat backward or forward, I keep moving my butt forward or backward, although that's partly - maybe largely - a function of the saddle design. If I tilt the saddle farther down, I feel as if I'm going to fall off; if I tilt it farther up, I get numb within 10 miles. If I move the saddle up or down, my knees hurt. Since any change in my saddle position increases my discomfort, I'm not about to change it.
But my hands hurt. When I set my bike up in the late '80s, the reco was for the 'bars to obscure the hub when on the drops. That is still what I (don't) see. Competitive Cyclist's tool says 56 cm TT, and that's what I've got.
Pull the seat back and lean forward more, you might have more weight on your hands. Straighten your arms instead, sure you'll have less weight there.
I think the first sentence may have it backwards. I know the 2nd is problematic - at least for me, straight arms put more stress on hands, arms, and shoulders and more weight on hands.
Yet how much your core works to hold up the torso weight makes more difference in weight on the hands than the saddle position.
I'm hoping that's true, and my experience is that, as long as I'm not too tired, the stronger my core is, the more comfortable I am on the bike and the less weight is on my hands.
I do find that pedaling all out seems to take all weight off my hands. I can't pedal all out for long, but I think pedaling effort does effect comfort.