Straight bars with twist or thumb shifters would probably help the tennis elbow. Part of my recovery was due to riding a recumbent with twist grips which in theory should be just as bad as brifters but weren't, as I wasn't gripping the bar nearly as tightly. You would not get as much improvement from the position change as I did but there would be some. Straight bars have the disadvantage of very few options for changing the hand position compared with drop bars, more of a problem on longer rides than shorter rides.