QSO near-zones are an important probe of the the ionization state of the IGM at z ~ 6-7, at the end of reionization. We present here high-resolution cosmological 3D radiative transfer simulations of QSO environments for a wide range of host halo masses, 10$\mathrm{<mrow\; data-mjx-texclass="ORD">10-12.5</mrow>}$ M_sun. Our simulated near-zones reproduce both the overall decrease of observed near-zone sizes at 6 < z < 7 and their scatter. The observable near-zone properties in our simulations depend only very weakly on the mass of the host halo. The size of the H II region expanding into the IGM is generally limited by (super-)Lyman Limit systems loosely associated with (low-mass) dark matter haloes. This leads to a strong dependence of near-zone size on direction and drives the large observed scatter. In the simulation centred on our most massive host halo, many sightlines show strong red damping wings even for initial volume averaged neutral hydrogen fractions as low as ~ 10$\mathrm{<mrow\; data-mjx-texclass="ORD">-3</mrow>}$. For QSO lifetimes long enough to allow growth of the central supermassive black hole while optically bright, we can reproduce the observed near-zone of ULAS J1120+0641 only with an IGM that is initially neutral. Our results suggest that larger samples of z > 7 QSOs will provide important constraints on the evolution of the neutral hydrogen fraction and thus on how late reionization ends.