Assuming you have single mode propagation (as suggested in the diagram) and that the overall structure is no more than a few wavelengths in size, I would recommend CST. The CST retagnular mesh is a natural for this kind of geometry (although curving surfaces are well represented with their Perfect Boundary Approximation, PBA, when needed). Also, you can get broad band frequency domain data with a single analysis (CST is time domain). One drawback is that CST must analyze three times, once for excitation at each of the three ports. However, with just three ports, that should not be too much of a problem.
If you have a graduate student working for a Ph. D., I would very strongly suggest the mode-matching approach. This particular problem would make for a very nice disertation. Analysis times would be on the order of a couple seconds per frequency, and maybe faster. Accuracy would be essentially exact.