Bond/Angle/Torsion/VdW energies DO NOT change as the uni-axial strain increases

Then your description of the symptom was not accurate. Energies do change, but only linearly.

It is difficult to relate the plots of yours and of the Ref’s; I would try to plot the same thing as the Ref. does, and see what they look like. I am not familiar with both models, but the differences may very well result from the stiffnesses of the two models you are comparing.