  Capitalizing on recent work, that clarifies the consistent use of
bosonization-debosonization methods to study Kondo-type quantum impurity models
even in nonequilibrium settings, we revisit the compactification procedure of
the two-channel Kondo model (by which it is rewritten more ``compactly'' using
the single-channel version of the model and exploiting separation and duality
between spin and charge) and uncover some hidden approximations that could
limit its range of validity. This complements and extends, for two or any even
number of channels, beyond previous work on the Toulouse limit of these models,
and reinforces the need for the use of an extended framework in these
calculations. We carry out a number of exact comparisons between the different
models, and show that keeping track of the, so-called, consistency factors
leads to full agreement between the compactified and original versions of the
model.
