Under MWI, this is so unsurprising that I'm having a hard time justifying performing the experiment except as a way of showing off cool things we can do with coherence.

Then the justification is simple; it either provides evidence in favour of MWI (and Copenhagen and any other theory that predicts the expected result) or it shatters all of them.

Scientists have to do experiments to which the answer is obvious - failing to do so leads to the situation where everybody knows that heavier objects fall faster than lighter objects because nobody actually checked that.