I'm confused by this post. You want to work on neck reining, so I am assuming you ride western, but you want to switch to a kimberwick? A kimberwick is a direct contact bit and therefore must be used with two hands, so you wouldn't be neck reining with a direct contact bit. Also, kimberwicks can be very severe if not used properly, so don't assume that they are less severe than a shank bit. And correct me if I'm wrong, but it sounds like you're using two hands while riding in a shank bit. If this is the case, that is probably the reason you are not getting the results you want. Shank bits work by using leverage, which can only be acheived by using one hand and a loose rein. If you're using two hands and direct contact on a shank bit, it wont work properly. Many people believe that snaffle bits can have a shank (ex. The tom thumb is referred to as a 'cowboy snaffle'), and they use direct contact with them, but it's simply not the case. Any bit with a shank, regardless of the mouthpiece, is a curb bit, not a snaffle, and should only be used with a loose rein.
To answer your question, kimberwicks can be very effective in achieving a proper carriage. On the sides of the kimberwick there are two holes for rein attachment. If you connect your reins to the lower hole, you'll have a little more leverage which is helpful is helping your horse collect. On the other hand, if you do ride western and wanted to use a shank bit, I'd recommend a low port barrel bit. These bits are great at helping a horse collect himself and when used properly (ie. One hand, loose contact!) are very mild.
It's all a matter of preference. I ride western (team penning and barrel racing), but I ride with an eggbutt snaffle because I prefer to ride two handed and my horse collects himself beautifully in it. It just takes a little bit of training. Good luck with whatever you choose!