Naked-eye limiting magnitude: mismatch between Wikipedia, online converter and Shaefer's formula
Being by no means an expert of light pollution, I still find my intermediate results worth sharing.
On the one hand, there is the Bortle Scale, and I find the flow chart from darksky.org the most accesible way (and probably it is also a reliable source):

This flow chart refers to the original publication by Bortle  from 2001 which was mentioned in the question. For all objects mentioned in a flow chart, one could determine their magnitude and obtain a magnitude-Bortle-scale conversion table (I might do that in a later edit).
On the other hand, there is a conversion site directly by a manufacturer of SQMs which converts ${\rm visual\,mags}/{\rm arcsecond}^2$ to ${\rm cd/m^2}$ according to the following formula:
$$[{\rm value\,in\,cd/m^2}]=    10.8\cdot 10^4 \cdot 10^{-0.4 \cdot [{\rm value\,in\, mag/arcsec^2}])}$$
The impression I got from my research is that there is no single, golden source publication linking NELM with physical properties such as ${\rm cd/m^2}$.
Last but not least, I stumbled up Roy Bishop's visibility factor (see German wikipedia) as more advanced (aka quantitiative) approach.