We've discussed the issues involved here many times so a search my uncover a lot of information.

Given your circumstances I suggest that you want to move the saddle BACK as far as you can which may include a seatpost with more offset or even a new frame/bike.

Consider the BB (bottom Bracket ) to be the centre of gravity on the bike. The more weight you have forwards of the BB the more weight you have on your arms/shoulders. The less weight you have forwards of the BB the less weight you have on your arms shoulders.

The quick and dirty way of assessing the fore/aft balance of your bike is the seat tube angle. A 73 degree seat tube angle is kind of neutral for a performance road bike. Bigger numbers (74, 75 degrees) are steep which places more weight on your hands/shoulders and smaller numbers (72, 71 degrees place less weight on your hands/shoulders.

Now that was an over generalisation yet in your case where taking the weight off your hands /shoulders is paramount then finding a bike with a slack (low number) seat tube angle is where you want to look.

Reach to the handlebars is an issue too yet the seat tube angle is far more important. A short reach but steep seat tube angle is still surprisingly uncomfortable. A long reach can be surprisingly comfortable if the seat tube angle is relaxed.