I'm about your size and when I was shopping bikes I was concerned that my back wouldn't tolerate a road bike. So I spent time looking at flat bar bikes and the so called "plush" road bikes. But I ended up buying a true road bike and setting it up a little, and have found it to be comfortable and very efficient on longer rides. If you want to do something as long as a half century that might be something you consider. You can get a decent used or entry level model in your price range.