> But if their problem is not being able to stomach the "just-because" explanations that every QM resigns to using to explain wtf complex conjugation has to do with reality

Having studied both engineering and physics, I can tell you that there is nothing observable in the universe that requires complex arithmetic/algebra/theory. We use it because it makes the math a lot more convenient.

BTW, the use of complex math for real world applications goes way beyond QM, and predates it significantly. Engineers use it all the time: AC Circuit theory is full of it. As is electromagnetics. As is power (motors, etc). As is anything involving Fourier or Laplace Transforms (i.e. almost all engineering). You can come up with purely real mathematics to describe all of the above, but it would be tedious.