It isn't strain so much as an impossible angle, which would be cured by lowering the brakes as margrette and Becky suggested. My back actually feels better on the flat part of the bars or bent over lower in the drops...halfway up with my hands forward to kinda try to reach the brakes, the muscles pull over the screws in my back.

The brakes are unreachable on the hoods as well, I generally use them by wrapping my entire hand around the little plastic brake support thingies (what are those called?)