If either the particle properties or the fundamental constants were changing, then our laboratory measurements would be changing as well: according to these reformulations, over a ~14 year timescale (since 2009 or so), we would have noticed variations in the observed properties of these well-measured quanta that are thousands of times larger than our tightest constraints: of about 1-part-per-billion.
This argument doesn't sound very convincing with such a lack of precise explanations of the conditions. I'm really not convinced they've thought this through.
This struck me too, if you're relying on instruments that exist in a universe where its constants are changing to measure those constants, then it seems very natural to me that your measurements would not necessarily change.
The constants instruments use to measure other constants might change at the same rate, leaving measurement results constant.
Then again, I'm not a physicist, so I'm nowhere near an expert.
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