A rigorous but yet highly accurate and efficient numerical treatment of plane wave scattering by T-shaped planar corrugations through full-wave modal analysis is first presented in this paper, which entails the moment method using parallel-plate waveguide cavity Green's functions and a numerical spectral-domain Green's function for planar stratified media. Investigations in terms of both reflection-phase and dispersion diagrams are conducted. After validating with the commercial software package: CST Microwave Studio, this moment-method is in turn used to verify a formula derived by the transverse resonance technique (TRT) for the surface-wave propagation constant of corrugations in terms of the dispersion diagram. Correspondences between the reflection-phase and dispersion diagrams are then established by relating the high and low impedance frequencies in the former with the pass and stop bands of the latter. With the abovementioned formula, the way is paved for a novel derivation of explicit formulas for the reflection-phase of an incident plane wave impingent on the corrugations as closed-form analytic functions of the various parameters, even for oblique azimuth planes of incidence and for both TE and TM polarizations. Doing so, the high or low surface-impedance (AMC or AEC) properties of such corrugations can virtually be acquired instantly, thus providing incomparable speedup of the process of thorough reflection-phase characterization of AMC or high-impedance surfaces and soft surfaces, thus affording rapid designs of antennas and microwave devices that make use of them.