This theoretical modeling-and-simulation paper presents designs and projected performance of ~1500-nm silicon-on-insulator 2 x 2 Mach-Zehnder interferometer (MZI) optical crossbar switches and tunable filters that are actuated by thermo-optical (TO) means. A TO heater stripe is assumed to be on the top of each waveguided arm in the interferometer. Each strip-waveguide arm contains an inline set of N-fold coupled, phase-shifted Bragg-grating resonators. To implement accurate and realistic designs, a mixed full-vectorial mathematical model based upon the finite-element, coupled-mode, and transfer-matrix approaches was employed. The Butterworth-filter technique for grating length and weighting was used. The resulting narrowband waveguide-transmission spectral shape was better-than-Lorentzian because of its steeper sidewalls (faster rolloff). The metrics of crossbar switching, insertion loss (IL) and crosstalk (CT), were evaluated for choices of grating strength and TO-induced change in the grating-waveguide refractive index. The predicted ILs and CTs were quite superior to those cited in the literature for experimental and theoretical MZI devices based upon silicon nanobeam resonators. This was true for the Type-I and Type-II resonator addressing discussed here. Finally, we examined the TO-tunable composite filter profiles that are feasible by connecting two or more Type-I MZIs in an optical series arrangement. A variety of narrow filter shapes, tunable over ~2 nm, was found.