We have developed a model for analysing x-ray Thomson scattering data from high-density, millimetre-scale inhomogeneous plasmas created during ultra-high pressure implosions at the National Ignition Facility in a spherically convergent geometry. The density weighting of the scattered signal and attenuation of the incident and scattered x-rays throughout the target are included using radial profiles of the density, opacity, ionization state, and temperature provided by radiation-hydrodynamics simulations. These simulations show that the scattered signal is strongly weighted toward the bulk of the shocked plasma and the Fermi degenerate material near the ablation front. We show that the scattered signal provides a good representation of the temperature of this highly nonuniform bulk plasma and can be determined to an accuracy of ca. 15% using typical data analysis techniques with simple 0D calculations. On the other hand, the mean ionization of the carbon in the bulk is underestimated. We suggest that this discrepancy is due to the convolution of scattering profiles from different regions of the target. Subsequently, we discuss modifications to the current platform to minimise the impact of inhomogeneities, as well as opacity, and also to enable probing of conditions more strongly weighted toward the compressed core.