I too have struggled with how to remove trailer shake and I do have to agree with Larry on the assessment of the problem. First, I'm going to to challenge someone to explain how X-chocks which do nothing more than allowing lateral movement of the wheels, do anything more than the plastic wheel chocks since the problem is essentially up and down force being applied to the suspension and the trailer frame.
I've installed scissor jacks in front of and behind the axles for a total of eight scissor jacks. That did little to help the trailer shake. I've also used the aluminum screw jacks placed in various locations and adjusted snuggly, although my process wan't as detailed as Larry's. Regardless, with the screw jacks placed on solid pads or concrete and tightened one to two turns more after toughing the frame, that should be enough to at least offer some stabilization to the frame. I can even feel the vibrations when the Yorkies run through the trailer, and this thing is supposed to be built on 8" I-beams. The only thing that I have not tried is to crawl under the trailer and put the screw jacks in the center of the frame, and I simply refuse to do that. All that said, I give up.