Well, keep in mind -- at those power levels (some kW and up), strays (parasitics) matter. You cannot design an inverter without mitigating these effects. Remember that every wire/trace is inductance, of ballpark 1nH/mm. Less when wider (broad-facing arrangement) and closely spaced, or vice versa. It adds up, especially at high currents, fast rate of change, and large builds (e.g. IGBT modules vs. THT vs. SMT components). Which is part of the reason why larger converters simply can't run as fast. (Another part being, high voltage devices just don't switch as fast, either. The 3kV+ IGBTs usually take a few microseconds.) Understand what (stray) inductances and (device or other) capacitances are important, during which phases of the switching cycle.
This isn't an easy subject, it can take years of practice; be patient. Do smaller tests first, see how it works, make an intentionally bad circuit, add snubbers to fix it, etc.
I think the biggest problem with the type of multilevel inverter shown, is that each bridge needs an isolated supply, well enough isolated that it doesn't load down the switching edge from the proceeding stage. This is not easy to do; a typical isolation transformer of some kVA to MVA capacity, will have at least 10s of pF, up to some nF, of stray capacitance between the winding and the primary or core. And you will rarely if ever have isolated supplies handy; they must be isolated with an additional DC-DC converter stage, nearly doubling the complexity of the system -- and costing precious efficiency.
Tim