He has a book. I haven't read it, but I'm sure he must discuss this issue in it.

In any case, I'm sure you can come up with a definition of "measurement" that might make the Copenhagen Interpretation experimentally indistinguishable from MWI, but why? MWI is and always will be a simpler theory, and thus preferred by Occam's razor.

The problem with the Copenhagen Interpretation is that it is NOT a scientific theory. It is not a scientific theory because it is not falsifiable. It also builds non-fundamental things like "measurement" right into the fundamental laws of physics, which is absurd. Copenhagen is not falsifiable, because if I were to attempt to falsify it by demonstrating that a "measurement" did not cause the wave function to collapse, you could always assert that I had used the wrong definition of "measurement".

GRW, on the other hand, can be seen as a sub-interpretation of the Copenhagen Interpretation because it rigorously defines the term "measurement". I.e., entanglement of the particles in question with a "large enough" collection of additional particles. "Large enough" here needs some experimental tuning, but some day we may be able to perform these experiments and attempt to falsify GRW. Because we can falsify GRW, it IS a scientific theory.

Most other collapse interpretations that I have heard of can likewise be seen as sub-interpretations of Copenhagen, in that they define "measurement".

One of those sub-interpretations is the Wigner Interpretation, or the "consciousness causes collapse" interpretation. Counter to your previous assertion, we could in theory experimentally determine whether this is true via trained rats: (1) Train a rat to perform measurements, (2) kill the rat before it has a chance to tell you the results, (3) check to see whether wave function has collapsed. We can do this because there are experiments that will tell you if two particles are entangled or not.

Animal consciousness not good enough for "measurement"; it needs to be human? Okay, Nazis could in theory perform this experiment, as could future evil alien overlords.

Now let's go back to MWI: I think that many people have a misconception about MWI, and perhaps this is due to its name. (If we had stuck to the name "Everett Interpretation" perhaps that would have been better.) MWI doesn't really imply multiple worlds. It implies one very complicated superimposed world. It is also the simplest theory, as it does not add the complication of wave function collapse. Furthermore, it is completely consistent with every bit of data that has ever been collected.

Another misconception is that MWI asserts that the "other worlds" that fall out of it are "real". This is not the case. MWI is agnostic on this issue. For instance, Stephen Hawking is in favor of MWI, but he doesn't like the name, because he thinks that asserting that the "other worlds" are "real", rather than just mathematical artifacts of the theory, is not something that we can scientifically know.

Executive summary: MWI is the simplest theory, and is consistent with all data. By Occam's razor, we are required to give this theory preference until we have evidence that contradicts it.

The counter argument to the above is that the ontological cost of all these many worlds (or maybe even the complicated superpositions of state) is too great, and that this somehow violates Occam's razor.

Well, first of all it doesn't, since Occam's razor these days is almost always taken to prefer the SIMPLEST THEORY, regardless of additional philosophical worries like, "It's just creepy to think that there might be so many other worlds."

Furthermore, this objection is based on a misinterpretation of MWI. MWI is completely agnostic about the ontological status of these "other worlds". It's just a mathematical formulation for making scientific predictions. There are many cases in the history of science where "creepy" things fall out of the math, if we were to grant them the status of being ontologically "real", and yet we don't reject the theories because of this. E.g., virtual particles and advanced waves. Sometimes scientists at some point decide that mathematical artifacts of theories are "real". E.g., virtual particles. And at other times, they remain just mathematical artifacts. E.g. (maybe), advanced waves.

Are the other worlds in MWI "real"? You tell me! Science cannot answer that question. This does not imply that MWI isn't the best theory.