Recent investigations have shown that many parameters and assumptions made in the application of spectral ageing models to FR-II radio galaxies (e.g. injection index, uniform magnetic field, non-negligible cross-lobe age variations) may not be as reliable as previously thought. In this paper we use new VLA observations, which allow spectral curvature at GHz frequencies to be determined in much greater detail than has previously been possible, to investigate two cluster-centre radio galaxies, 3C438 and 3C28. We find that for both sources the injection index is much steeper than the values traditionally assumed, consistent with our previous findings. We suggest that the Tribble model of spectral ageing provides the most convincing description when both goodness-of-fit and physically plausibility are considered, but show that even with greatly improved coverage at GHz frequencies, a disparity exists in cluster-centre FR-IIs when spectral ages are compared to those determined from a dynamical viewpoint. We find for 3C438 that although the observations indicate the lobes are expanding, its energetics suggest that the radiating particles and magnetic field at equipartition cannot provide the necessary pressure to support the lobes, similar to other cluster-centre source such as Cygnus A. We confirm that small scale, cross-lobe age variations are likely to be common in FR-II sources and should be properly accounted for when undertaking spectral ageing studies. Contrary to the assumption of some previous studies, we also show that 3C28 is an FR-II (rather than FR-I) source, and suggest that it is most likely a relic system with the central engine being turned off between 6 and 9 Myrs ago. ; Comment: 20 pages, 9 figures, 8 tables. Accepted for publication in MNRAS