The first observation is that the original Moog software appears to be using a preload of 0.6/4 = 15%. The 0.6 is approximate average of the ± currents on the graph on page 2 left side.
Per Austin's comment Moog had the current limit set at 3.6A. However, it appears from the Tekniker manual page 22 figure 33 that they raised this limit to 4.0A. If my understanding is correct the current limit should be reduced back to the specified 3.6A. The current limit was set to meet the requirements of limiting the torque to prevent damage to the cables and Hoses. We should probably be using the same preload.
The plots on page 3 show negligible preload. It appears that the values are ~+/-0.05 amps or about 1%. It appears in the Tekniker manual on page 23 figure 34 that the preload was set to Tq = 0/100. Does this mean no preload or? These plots show oscillations between positive and negative torque. Whenever this happens instability is expected produced by the small gap between the gears.
There is a reasonable chance that increasing the preload, tq, will resolve this issue. The other possibility is that we should reduce the gains. The rapid oscillations imply high gains which are unnecessary. Figure 34 appears to show a gain, Kp of 10/100 (10%?). This is a fairly small gain but we may try reducing it. We do not need a fast system. We need an accurate and stable one.