The maps presented in Paper I are here used to infer the variation of the column densities of HCO⁺, DCO⁺, N₂H⁺, and N₂D⁺ as a function of distance from the dust peak. These results are interpreted with the aid of a crude chemical model that predicts the abundances of these species as a function of radius in a spherically symmetric model with radial density distribution inferred from the observations of dust emission at millimeter wavelengths and dust absorption in the infrared. Our main observational finding is that the N(N₂D⁺)/N(N₂H⁺) column density ratio is of order 0.2 toward the L1544 dust peak as compared to N(DCO⁺)/N(HCO⁺) = 0.04. We conclude that this result, as well as the general finding that N₂H⁺ and N₂D⁺ correlate well with the dust, is caused by CO being depleted to a much higher degree than molecular nitrogen in the high-density core of L1544. Depletion also favors deuterium enhancement, and thus N₂D⁺, which traces the dense and highly CO-depleted core nucleus, is much more enhanced than DCO⁺. Our models do not uniquely define the chemistry in the high-density depleted nucleus of L1544, but they do suggest that the ionization degree is a few times 10^-9 and that the ambipolar diffusion timescale is locally similar to the free-fall time. It seems likely that the lower limit, which one obtains to ionization degree by summing all observable molecular ions, is not a great underestimate of the true ionization degree. We predict that atomic oxygen is abundant in the dense core and, if so, H₃O⁺ may be the main ion in the central highly depleted region of the core.