We have had our rear kitchen model for 6 years now, towed it around 35K miles over much of the country and part of Canada. We have never had a broken dish or anything else. Things do move sometimes but that is to be expected with the roads we have. Lots of things can cause your problem like overinflated tires, suspension, weight distribution, etc.
To answer your question, I would think the Trail Air pin box would more beneficial as it will add some cushioning between the truck and the trailer. I would also look at adding shocks if that did not get the results you want. Ours came with them so not sure how much of an improvement they would be. A little bit of overkill, but about 3 years ago I decided to do some upgrades that I thought might help extend the life of our fifth wheel. I added a Center Point air suspension system which was a Trail Air product before Lippert bought them which did help smooth out the ride even more. Later I sold the B&W and got a Trailer Saver BD3 air ride hitch which really cuts out the jolting interaction between the truck and the trailer. In addition, I had a set of Air Lift air bags from a previous truck so I put them on the GMC for no good reason other than I had them. I'm not sure if they would help with your situation or not.
I think you are on the right track by trying to isolate the truck and trailer with the Trail Air. You didn't say, but if you have some bucking or chucking, which is not good for a rear kitchen, or any other type for that matter, the Trail Air can help with that. My honest opinion is that an air ride hitch would be more beneficial, but, it costs more. If that fails you may have to look at the trailer's suspension. There are a lot of options for things to try but they also can cost a bit. Good luck and let us know how it goes.