3D test particle simulations of historic ground level enhancement (GLE) events are performed to investigate the propagation and distribution of solar protons within the heliosphere. The test particle model, which includes drift effects, is also used to explore the influence a heliospheric current sheet (HCS) has on the propagation of protons. Historic GLEs with a source location close to and far from the HCS, as well as poorly and well-connected events are considered. The modelling is performed for high energy (300$-$1200 MeV) protons to represent the energetic conditions under which these GLEs occur. The derived intensity profiles at 1AU are compared to observations from HEPAD onboard GOES as well as neutron monitor data. We present the results from two of our historic GLE simulations here: GLE 42 and 65. Our results suggest that the HCS plays a significant role in distributing energetic particles throughout the heliosphere. The particle transport along the HCS is most efficient when the injection location is very close ($<$10$^{\circ}$) to it. GLEs with flares that are within 10$^{\circ}$ of the HCS all have significantly larger neutron monitor increases than those with flares further away, suggesting that the proximity of the flare to the HCS strongly affects the severity of the event at Earth.