Take a close look at the Horizontal Stabilizer system. We had an L4 with an improperly installed horizontal stabilizer. There is a set pin that attaches the right and left side assemblies in the tail cone. This pin was loose. As a result one side was moving slightly with respect to the other side. Grab one side of the stabilizer and see if there is any play with respect to the other side. I do not believe that any play is allowed. We felt a similar lurching in our airframe when fully loaded at level max cruise speed. Once we rebuilt the assembly the problem went away.
