If you want a bike with drop bars, buy a bike with drop bars. While it is possible to modify a bike with flat bars to drops, it is expensive. If you go with a flat bar bike, you will regret it.

My suggestion? Salsa Vaya, Jamis Renegade, Jamis Quest comp, Giant AnyRoad, Kona Rove, All City Space Horse, All city Mr. Pink, Surly Straggler, Surly Pacer, or Fairdale Weekender drop.

This is not an exhaustive list, but rather a starting point. I am sure there are other drop bar road bikes that can handle your weight that you can find.