A late end to reionization at redshift z ≃ 5.3 is consistent with observed spatial variations in the Ly α forest transmission and the deficit of Ly α emitting galaxies around extended Ly α absorption troughs at z = 5.5. In this model, large islands of neutral hydrogen should persist in the diffuse intergalactic medium (IGM) until z ≃ 6. We use a novel, hybrid approach that combines high-resolution cosmological hydrodynamical simulations with radiative transfer to predict the incidence of strong 21-cm forest absorbers with optical depths τ_21 > 10^−2 from the diffuse IGM in these late reionization models. We include the effect of redshift space distortions on the simulated 21-cm forest spectra, and treat the highly uncertain heating of the pre-reionization IGM by soft X-rays as a free parameter. For a model with only modest IGM pre-heating, such that average gas kinetic temperatures in the diffuse IGM remain below |$T_{\rm K}\simeq 10^{2} \rm \, K$|⁠, we find that strong 21-cm forest absorption lines should persist until z = 6. For a sample of ∼10 sufficiently radio-loud background sources, a null-detection of 21-cm forest absorbers at z ≃ 6 with SKA1-low or possibly LOFAR should provide an informative lower limit on the still largely unconstrained soft X-ray background at high redshift and the temperature of the pre-reionization IGM.