-Right (and only)after work, his back slightly contracts if you press a certain point on his back. Could it be the Crates barrel saddle we're using? Past owners said that was the saddle the had been using with him. Would a reining saddle be better?
Others are providing some good advice, so I will only comment on this one piece. Since the horse did well going on trail away from the barn, I am tempted to think it is not a saddle issue. Supporting that is that the previous owners used the same saddle.
Saddle fit is still something worth checking out. Also consider your saddle pad. I had a good fitting saddle with a high quality pad. The pad was thick felt with stitching up the middle. What I didn't realize at first was when I sat in the saddle, the back of the pad would push apart and the stitching would rub on the horse. A light saddle blanket under the pad fixed that. It is probably not your problem, but I point to it as an example.
Also not that a "barrel" or "reining" saddle generally refers to the style of the part _YOU_ sit on. What is more important are thing like tree style, angle of the bars, and size of the gullet... the parts that sit on your horse's back. Don't get wrapped up in "barrel" "reining" "ranch" etc. If you are concerned about saddle fit, have someone knowledgeable take a look and determine the correct size.
An analogy - if you wear a size 12 shoe, it wouldn't matter if you had a sneaker, oxford or loafer. A size 10 would be tight and a size 13 would be too big. Fit is more important than style.