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.