Swapping the stem may make the riding more comfortable, but you may want to look at other things too
Horizontal position of the seat - most seats will be able to be adjusted forwards or backwards. But if you change the position of the seat, relative to the cranks, you need to think about how this will affect your stroke.
Handlebar width - if the handlebars are too wide you may feel like you are reaching too far forward, when in fact you are reaching too far out. A simple check is to stand across your bike in front of a mirror, put your hands on the hoods, and see how closely your handlebars match the width of your shoulders.
Frame size - it's possible you have a bike that's too big for you. Although this is the most expensive thing to change, after riding a bike like that for a couple of years before finally spending the money on a properly fitted frame, I believe it's worth the money for the extra enjoyment you get from riding.