You might try some mustache bars or some other bar where you can get your hands oriented differently. IMO, palm down that one gets with flat bars puts my wrist in its weakest position. It's why I dislike them so much. Though I know I'm probably in the minority on that opinion.
Finding something other than drops that give your hands and wrist a different position than the current flat bars will allow you to only have to change the bars and maybe the stem length and still use your current shifters and brake levers.