The HCN, HCO+, and HNC molecules are commonly used as tracers of dense star-forming gas in external galaxies, but such observations are spatially unresolved. Reliably inferring the properties of galactic nuclei and disks requires detailed studies of sources whose structure is spatially resolved. We compare the spatial distributions and abundance ratios of HCN, HCO+, and HNC in W49A, the most massive and luminous star-forming region in the Galactic disk, based on maps of a 2 (6.6 pc) field at 14 (0.83 pc) resolution of the J=4-3 transitions of HCN, H13CN, HC15N, HCO+, H13CO+, HC18O+ and HNC. The kinematics of the molecular gas in W49A appears complex, with a mixture of infall and outflow motions. Both the line profiles and comparison of the main and rarer species show that the main species are optically thick. Two clumps of infalling gas appear to be at ~40 K, compared to ~100 K at the source centre, and may be ~10x denser than the rest of the outer cloud. Chemical modelling suggests that the HCN/HNC ratio probes the current gas temperature, while the HCN/HCO+ ratio and the deuterium fractionation were set during an earlier, colder phase of evolution. The data suggest that W49A is an appropriate analogue of an extragalactic star forming region. Our data show that the use of HCN/HNC/HCO+ line ratios as proxies for the abundance ratios is incorrect for W49A, suggesting the same for galactic nuclei. Our observed isotopic line ratios such as H13CN/H13CO+ approach our modeled abundance ratios quite well in W49A. The 4-3 lines of HCN and HCO+ are much better tracers of the dense star-forming gas in W49A than the 1-0 lines. Our observed HCN/HNC and HCN/HCO+ ratios in W49A are inconsistent with homogeneous PDR or XDR models, indicating that irradiation hardly affects the gas chemistry in W49A. Overall, the W49A region appears to be a useful template for starburst galaxies.