In the first paper of this series, we proposed a new framework in which to model the chemical evolution of globular clusters. This model is predicated upon the assumption that clusters form within an interstellar medium enriched locally by the ejecta of a single Type Ia supernova and varying numbers of asymptotic giant branch stars, superimposed on an ambient medium pre-enriched by low-metallicity Type II supernovae. Paper I was concerned with the application of this model to the observed abundances of several reactive elements and so-called non-metals for three classical intermediate-metallicity clusters, with the hallmark of the work being the successful recovery of many of their well-known elemental and isotopic abundance anomalies. Here, we expand upon our initial analysis by (i) applying the model to a much broader range of metallicities (from the factor of 3 explored in Paper I, to now a factor of ∼50; i.e. essentially, the full range of Galactic globular cluster abundances; and (ii) incorporating a broader suite of chemical species, including a number of iron-peak isotopes, heavier -elements and fluorine. While allowing for an appropriate fine-tuning of the model input parameters, most empirical globular cluster abundance trends are reproduced; our model would suggest the need for a higher production of calcium, silicon and copper in low-metallicity (or so-called ‘prompt’) Type Ia supernovae than predicted in current stellar models in order to reproduce the observed trends in NGC 6752, and a factor of 2 reduction in carbon production from asymptotic giant branch stars to explain the observed trends between carbon and nitrogen. Observations of heavy-element isotopes produced primarily by Type Ia supernovae, including those of titanium, iron and nickel, could support/refute unequivocally our proposed framework, although currently the feasibility of the proposed observations is well beyond current instrumental capabilities. Hydrodynamical simulations would be necessary to study its viability from a dynamical point of view.