Analytic expressions are obtained for particle and heat fluxes in the Pfirsch-Schlüter regime for tokamak plasmas with elliptical cross-section flux surfaces, allowing for outward toroidal equilibrium shifts. The results are then used in an elliptical metric 1D transport code, and rather striking differences in the plasma profiles are found to result from cross-section shaping for the comparative example of tokamak start-up. The Pfirsch-Schlüter diffusion flux of heavy impurities is then compared analytically for elliptical and circular cross-sections, and quantitative estimates are made of the extent to which ellipticity can retard impurity accumulation in a device such as Doublet II-A.