Is the accurate model that complex, though? An electron is a standing wave: one could show the first two standing waves on a drum and say these are the lowest two electron energy levels. Higher levels create more sophisticated waves, and non-flat potential adds more complexity, but the idea remains the same.
Yes, you are right, standing waves is the exact model that is used. All the measurement problems with e.g. location are just a consequences of that, some properties of a standing wave may be "smeared all over" the wave, like its location. And some interactions with the wave will change it. Quantized things are just standing waves of different order or "frequency" in a confined system.
It's own thing, and thinking of it as a classical wave or a classical particle isn't accurate. You go through the math and the experiments and try to build and intuition for what it is in its own right without reference to classical analogies.
