  Alexander polynomial arises in the leading term of a semi-classical
Melvin-Morton-Rozansky expansion of colored knot polynomials. In this work,
following the opposite direction, we propose how to reconstruct colored
HOMFLY-PT polynomials, superpolynomials, and newly introduced $\widehat{Z}$
invariants for some knot complements, from an appropriate rewriting,
quantization and deformation of Alexander polynomial. Along this route we
rederive conjectural expressions for the above mentioned invariants for various
knots obtained recently, thereby proving their consistency with the
Melvin-Morton-Rozansky theorem, and derive new formulae for colored
superpolynomials unknown before. For a given knot, depending on certain
choices, our reconstruction leads to equivalent expressions, which are either
cyclotomic, or encode certain features of HOMFLY-PT homology and the
knots-quivers correspondence.
