If you have poor core stability (and most cyclist do) then a pro-roadie drop position will be uncomfortable, as you'll be moving a lot of weight to your hands. If you're supporting your torso with your hands, it's going to hurt like crazy.
Look at modern road bikes for, uh, 'enthusiasts' - the head tube is pretty long. This makes it easier to use drop bars and get the benefit without being a yoga deity.
I went out on my Tricross for a ride for the first time in months on Sunday and suffered like crazy. Last November (the last time I rode it - excuses: house move, second nipper, work) I din't have a problem on a 120 mile overnight ride using the drops. A 20 mile ride nearly killed me this weekend.
I'd look to try a more upright position, shallower drop bars (FSA makes some lovely bars in up to 44cm - try a pair, they're better than every other FSA component I've ever used and thrown away put together) and proper advice from a roadie shop on bar and brake position before ditching drops and going for flat bars.
Why all this? Well, despite what's been said above, drops are actually pretty damn amazing in a headwind. Aerodynamics matter a lot more when you're riding on the road, and being able to hide from the wind a little makes an enormous difference. And yes, I know it matters most at 25mph and above, but even if you're plodding at 12mph into a 15mph headwind, that's still 27mph of apparent windspeed you have to contend with.
Hope this helps. Rather than dropping loads on a new bar and STI set up, tinker a little with what you have, and find a good road shop to go to. Pay for the bike fit if needs be. It's worth it.
 Of course, this also applies to rando bars and similar - basically, if you can make your frontal profile nice and teeny, you're winning.[/edit]