The Lidov-Kozai (LK) mechanism plays an important role in the secular evolution of many hierarchical triple systems. The standard LK mechanism consists of large-amplitude oscillations in eccentricity and inclination of a binary subject to the quadrupole potential from an outer perturber. Recent work has shown that when the octupole terms are included in the potential, the inner binary can reach more extreme eccentricities as well as undergo orientation flips. It is known that pericentre precessions due to short-range effects, such as General Relativity and tidal and rotational distortions, can limit the growth of eccentricity and even suppress standard (quadrupolar) LK oscillations, but their effect on the octupole-level LK mechanism has not been fully explored. In this paper, we systematically study how these short-range forces affect the extreme orbital behaviour found in octupole LK cycles. In general, the influence of the octupole potential is confined to a range of initial mutual inclinations itot centred around 90° (when the inner binary mass ratio is ≪ 1), with this range expanding with increasing octupole strength. We find that, while the short-range forces do not change the width and location of this 'window of influence', they impose a strict upper limit on the maximum achievable eccentricity. This limiting eccentricity can be calculated analytically, and its value holds even for strong octupole potential and for the general case of three comparable masses. Short-range forces also affect orbital flips, progressively reducing the range of itot within which flips are possible as the intensity of these forces increases.