Previous proposals to permit non-exponential free-path statistics in radiative transfer have not included support for volume and boundary sources that are spatially uncorrelated from the scattering events in the medium. Birth-collision free paths are treated identically to collision-collision free paths and application of this to general, bounded scenes with inclusions leads to non-reciprocal transport. Beginning with reciprocity as a desired property, we propose a new way to integrate non-exponential transport theory into general scenes. We distinguish between the free-path-length statistics between correlated medium particles and the free-path-length statistics beginning at locations not correlated to medium particles, such as boundary surfaces, inclusions and uncorrelated sources. Reciprocity requires that the uncorrelated free-path distributions are simply the normalized transmittance of the correlated free-path distributions. The combination leads to an equilibrium imbedding of a previously derived generalized transport equation into bounded domains. We compare predictions of this approach to Monte Carlo simulation of multiple scattering from negatively-correlated suspensions of monodispersive hard spheres in bounded two-dimensional domains and demonstrate improved performance relative to previous work. We also derive new, exact, reciprocal, single-scattering solutions for plane-parallel half-spaces over a variety of non-exponential media types.