Try converting a carbon road bike with Bullhorns. I think this is what you are after. Maybe install some Paul Component thumbies for shifting and put TT brake levers. I'd recommend Dura Ace TT brake levers and Syntace Stratos bars. You can thank me later.

Handle bars really dictate your riding position so this directly influences speed. Drop bars are versatile: fast, comfy, three great hand positions maybe even 4 if you don't have those silly bends. With Drop bars, I am slowest on the flat, fast on top of the levers and Supa fast on the drops. Flat bars, you are only in one position. So you don't the option to go from slow to fast to lightspeed fast. With bullhorns you can. You also have about 3 positions: the flats(slow), the middle of the horns(fast) and the end(going back in time FAST!) PLUS!!! you can pull on them to generate loads of power!!!! This is something that bullhorns got over drop bars. I am going to build a multi speed road bike with bullhorns. I got small hands so reaching for the levers on drop bars are a pain in the butt, but TT levers generally have reach adjustments and I just feel a whole lot more comfortable with them.

Give it a try. I think this can be a whole new bike category.