That experiment sounds very problematic to me. He says "After you measure the electron’s spin about the x-axis, have someone fully reverse the physical evolution.... Such reversal would be applied to everything: the electron, the equipment, and anything else that’s part of the experiment.".

There is no explanation of the mechanics of how he thinks such a time-reversal could be implemented. We simply don't have the fine control over the quantum state of the entire measurement apparatus. In fact, the very assumption that quantum theory is even the true/applicable state of affairs at this macro scale is the kind of thing that many Copenhagenists dispute.

Conversely, if it were possible to have such a fine control over the entire system including the very equipment used to perform the measurement, well then, you might as well simply make a quantum measurement of the larger quantum system which includes that apparatus! There would be different outcomes depending on whether collapse has or has not yet occured.

It seems like whether or not this experiment even makes sense relies somewhat on whether MWI is true. Ultimately I think the very description of this experiment makes hidden assumptions, which beg the same question it is trying to answer.

And even if you do, then the only viewpoint you will have really falsified is one which postulates that (a) the state vector collapse is caused by consciousness, and (b) concludes that therefore any consciousness has to do the trick, even one simulated on a quantum computer. I have met exactly zero physicists who'd treat (a) seriously, but even if you believe in (a), (b) still doesn't need to follow (someone could believe that only real human brain makes the magic happen).

(I assume you were referring to experiment 3. from Deutsch's "Three experimental implications of the Everett interpretation in Quantum Concepts in Space and Time.")