I spend the bulk of my time on the off road forums since I enjoy riding off road a great deal. By off road, that doesn't mean "mountain biking" although many times singletrack is involved, it does mean more off pavement though. I do still enjoy road riding and I own several "road oriented" bikes. I use drop bars off road a lot. Granted they are not typical, they are Salsa Woodchippers, they have some width to them, some sweep or flare but properly set up they are with a doubt the most comfy of any bar I use. Ragley has a similar bar out now called the Luxy. Woodchippers give me the leverage to handle the bike and control it when needed. I can slip into the drops and ride comfy there, then switch positions to the top of the bar or even to the hoods. You can play with the tilt or angle to get the drop and flare of the bars perfectly suited to you. I'm building a Vaya touring bike (frame should be here next week) and Woodchippers are the only thing I would consider. They work with bar ends, or STI set ups. Others I know have them on their road and gravel machines and a few on their touring machines.

Drops, flats, or off road drops...you have a lot of options and this doesn't take into account the trekking and other swept bars on the market. I'd suggest the Woodchippers though as a good alternative if you like drop bars but also like flat bars with a bit of sweep. Just realize they are not road drops and need their own set up. The flats off the drops usually need to be no more than an inch below your seat, usually higher or about where flat bars would be.