In this paper we use observations of molecular tracers in metal-rich and alpha-enhanced galaxies to study the effect of abundance changes on molecular chemistry. We selected a sample of metal-rich spiral and star-bursting objects from the literature, and present here new data for a sample of early-type galaxies (ETGs) previously studied by Crocker et al. We conducted the first survey of carbon monosulphide (CS) and methanol emission in ETGs, detecting seven objects in at least one CS transition, and methanol emission in five ETGs. We find that ETGs whose gas is dominated by ionization from star formation have enhanced CS emission, compared to their hydrogen cyanide (HCN) emission, supporting the hypothesis that CS is a better tracer of dense star-forming gas than HCN. We suggest that the methanol emission in these sources is driven by dust mantle destruction due to ionization from high-mass star formation in dense molecular clouds, but cannot rule out a component due to shocks dominating in some sources. We construct rotation diagrams for each early-type source where at least two transitions of a given species were detected. The rotational temperatures we derive for linear molecules vary between 3 and 9 K, with the majority of sources having rotational temperatures around 5 K. Despite the large uncertainty inherent in this method, the derived source-averaged CS and methanol column densities are similar to those found by other authors for normal spiral and starburst galaxies. This may suggest dense clouds are little affected by the differences between early- and late-type galaxies. Finally, we used the total column density ratios for both our ETG and literature galaxy sample to show for the first time that some molecular tracers do seem to show systematic variations that appear to correlate with metallicity, and that these variations roughly match those predicted by chemical models. Using this fact, the chemical models of Bayet et al. and assumptions about the optical depth we are able to roughly predict the metallicity of our spiral and ETG sample, with a scatter of approximate to 0.3 dex. We provide the community with linear approximations to the relationship between the HCN and CS column density ratio and metallicity. Further study will clearly be required to determine if this, or any, molecular tracer can be used to robustly determine gas-phase metallically, but that a relationship exists at all suggests that in the future it may be possible to calibrate a metallicity indicator for the molecular interstellar medium.