The evolution of star-forming core analogues undergoing inside-out collapse is studied with a multi-point chemodynamical model which self-consistently computes the abundance distribution of chemical species in the core. For several collapse periods the output chemistry of infall tracer species such as HCO+, CS, and N2H+, is then coupled to an accelerated Lambda-iteration radiative transfer code, which predicts the emerging molecular line profiles using two different input gas/dust temperature distributions. We investigate the sensitivity of the predicted spectral line profiles and line asymmetry ratios to the core temperature distribution, the time-dependent model chemistry, as well as to ad hoc abundance distributions. The line asymmetry is found to be strongly dependent on the adopted chemical abundance distribution. In general, models with a warm central region show higher values of blue asymmetry in optically thick HCO+ and CS lines than models with a starless core temperature profile. We find that in the formal context of Shu-type inside-out infall, and in the absence of rotation or outflows, the relative blue asymmetry of certain HCO+ and CS transitions is a function of time and, subject to the foregoing caveats, can act as a collapse chronometer. The sensitivity of simulated HCO+ line profiles to linear radial variations, subsonic or supersonic, of the internal turbulence field is investigated in the separate case of static cores. ; Comment: Accepted to MNRAS; 20 pages, 13 figs