  Following up on the systematic compactification of the two-channel Kondo
model (and its multichannel extensions; see
$\href{https://doi.org/10.48550/arXiv.2308.03569}{\textsf{companion paper I}}$)
and the demonstration of its validity over the past proposal of
compactification, we resort to a study of scaling using Anderson's simple poor
man's procedure to carry out a comparative study of these two and the original
model. By doing so we unveil a universal agreement among the three models in
how they flow upon scaling, and suggest the general limits of such a
concordance. In this way we further elucidate the conditions under which the
standard simplifications implicit in many bosonization-based mappings
(particularly of quantum impurity models) can be used reliably, and when the
consistent bosonization-debosonization approach is needed.
