This is an excellent, balanced review of the state of Montessori education research, published 3 days before a longitudinal study that addresses some of the issues raised and available at Frontiers in Psychology, titled Montessori Preschool Elevates and Equalizes Child Outcomes: A Longitudinal Study.
Additional research is discussed in Lillard (2017) Montessori: The Science Behind the Genius, chapter 11, 3rd edition (Oxford University Press).
In response to one issue raised: I think Montessori is a system, like culture, and therefore that teasing apart "the element" or even set thereof that creates better outcomes might be a fool's errand.
your last point there is a good one. Taking isolated element(s) from Montessori and using them in a normal classroom, divorced from other elements, may very well not work. But of course it might, and we won't know until it has been tested. If Montessori can produce better results, but for whatever reasons isn't widely implemented, I think it's at least worth a shot trying to figure out if any specific components are making the difference, and secondly, if transporting those elements into a standard classroom can offer benefits. Even if co-opting specific features didn't work, we would have learnt that the Montessori system is what matters, which is useful info too.
Thanks also for the pointing out your recent paper - I hope our readers find it interesting.