>The Copenhagen Interpretation is not even a fully-fledged interpretation, because it uses undefined, unscientific terms like "measurement" to determine when a probability wave collapses.

No, measurement is just a poor choice of name for a type of interaction some matter can have with other matter. I'm a wave function, and sometimes I have a measurement interaction with other wave functions and that causes collapse. When wave functions of random environment particles do the measurement and cause (seemingly) spontaneous collapse, we call it decoherence and its a serious drag on building quantum computers.

I'm not advocating for Copenhagen, but it is not inconsistent for the reasons you stated. Outside the paper linked here, I'm unaware of any inconsistency in the Copenhagen interpretation.