Too weird! I just went through this very issue myself!
I had a Brooks "S" saddle that I liked but it had short rails and could not be pushed back much. I felt generally comfortable on my bike, but I did notice that i was never comfortable riding in the drops.
I got a new Brooks saddle that was wider for my sitbones, and coincidentally it had longer rials enabling me to shove my saddle back about 1 1/2" further than before. I was afraid this would make my reach too long, but it didnt'. Instead, it made my torso fold down and forward more in a comfortable way, actually making the reach more comfy for me. Odd concept, but my DH had explained it to me and sure enough it was true- for me anyway. It felt GREAT, and suddenly my legs had more power to "get behind" my pedal strokes. I can spin up the hills now with much less leg burnout.

But the funniest thing of all was this- after a day or so of riding with my new further back saddle, I started just finding myself happily riding along in the drops- without even having realized I had put my hands there! Suddenly I was riding in the drops naturally all the time without even thinking about it. Riding in the drops is now actually the MOST comfortable riding position I have, as opposed to being the position I always avoided. It's great because now I can alternate hand/body positions way more and avoid fatigue on long rides.

So yeah, SHOVE that saddle back girl, and give it a try!