Solar thermochemical hydrogen (STCH) produced by heat-driven water-splitting is a promising route for producing green hydrogen and other zero-emission synfuels. However, the efficiency of STCH must be dramatically increased for it to make an impact on decarbonization efforts. We have previously presented a novel Reactor Train System (RTS) for significantly increasing the efficiency of STCH by employing heat recovery from the redox material and efficient gas exchange processes. In this paper we present a higher-fidelity model for the RTS that accommodates the slow heat diffusion through the STCH redox material. For this purpose, a novel method is introduced for transient modelling of radiative heat in participating media. This method, called GREENER: Generalized Radiation Exchange Factors and Net Radiation, combines the accuracy of Monte Carlo Ray Tracing with the low computational cost of the P1 or Rosseland diffusion approximations. Along with STCH, GREENER has application for modelling volumetric solar receivers, high temperature heat recovery systems like heat exchangers and regenerators, and packed bed reactors. Using the GREENER method, the RTS counterflow radiative heat exchanger is shown to achieve heat recovery effectiveness greater than 70%. The performance of non-uniform porous redox morphologies is evaluated, and high-performing configurations are identified.