Recently, Williams and Houston developed a near-field acoustic holography (NAH) method for generic cylindrical cavities [Proc. Internoise 96, 2553--2558]. Previously, cavity NAH methods required restrictions or gross assumptions, which limited their use to specific cases. The Williams--Houston method, on the other hand, is valid inside any practical cylindrical boundary. The method, though, requires prior measurement of the near field of all boundaries, whether they contain sources or not, even when boundaries are locally reacting with a known acoustic impedance. Also, because of singularities in the Green's function used, reconstructions could not be performed at some frequencies. This work is based on the Williams--Houston method, and presents several significant improvements and contributions. Most importantly, scattering off locally reacting cavity boundaries is accounted for in the Green's function, reducing the required number measurements and processing, for a given resolution. As well, Green's functions are solved for with consideration given to the uniqueness and existence of the acoustic field to allow reconstructions to be performed over a continuous range of frequencies. A set of cavity NAH Green's functions are developed in Cartesian coordinates, extending the method to parallel walled rectangular (box) cavities. Reconstruction results comparing the methods will be presented.