No experience with the K-Wings. Sorry. I'll say that the flat areas look like they'd be more carpal-tunnel friendly than plain round bars; but IME once you start down the ergo path, you've already arrived at the other end (you just don't know it yet.) But I'll say it here just because sooner or later somebody will. You don't need ergonomic aids if you have an ergonomic bike. With apologies to the original author for my manglement of the following:
1. I love my lightweight responsive upright and have no pain when riding
2. Aerobars so I can take the weight off my hands more
3. padded tape
4. extra padding in the gloves
5. Raise the bars
6. Fat foam handlebar tape
7. ...with two layers of foam pipe insulation over the top...
8. sell that bike, get recumbent. Problem solved.

YMMV, but that's the route I took, including all the intermediate stops. I hope the K-Wings work for you, they're a lot cheaper than a recumbent.