My knees hit my gut too. If you have copious abdominal circumference issues, it happens.
I also think that you should adjust your handlebars so that you can spend most of your time riding with your hands on or around the hoods. As P Diddy indicated, you should not have to ride in the drops to apply the brakes. Your hands will hurt at first, but if you move them around a lot, changing where you put the weight on your hands, you will get used to it rather fast.
Most of the time, I ride with my hands on the backs of the hoods, and can apply them just fine using the hoods like pistol-grips. I only use the drops for fighting a stiff wind, seeing how fast I can go down a big hill, and when I'm getting tired and want to lean down more to hit my hamstrings more (gives quads a little relief). You should be able to apply the brakes just fine from there. If you can't reach that far, they make spacers that make the gap between your brakes and the handlebars closer. They started making them a few years ago for women with smaller hands, but I see them on bikes owned by guys all the time now. Not everyone can palm a basketball. If my hands were any smaller, or I had arthritis, I would get spacers for sure.
One thing that I have noticed, is that a lot of us Clydes that like road bikes can bend forward a lot further if we stretch out more forward than down. My knees don't hit my gut, and I don't feel as cramped in general when I go farther out, than down. Lots of clydes ride with aero-bars for this reason (they also save your hands and back, since they put weight on your arms).
Hope this helps.