I wonder if you are not stuck with the difference between osculating and mean parameters.
Theories often rely on very simplified equations and are expressed in some kind of mean parameters (which depend on the theory) that remove all short period terms. When dealing with classical propagation, like numerical propagation for example, you get all these harmonics back.
In some cases, harmonics are really huge, see for example this thread and the eccentricity plot, in this case the short period terms are larger than the mean elements. Perhaps as you pick several points around the orbit you see short periods?