Perhaps you need a more upright position to start with on the bike? You can get riser stems that will lift up the bars.

The bike may "fit" you perfectly, but be unsuitable because it is too agressive (ie. you need to bend down to low to the bars, and bend you neck to look forwards). A riser stem would keep the same correct fit on the bike, but lift up your torso, allowing your head to be more on top of your shoulders and not craning upwards.

Are you able to comfortably get into the drops now? If you can't comfortably ride a ways in the drops, then a riser would probably be good.