It is well known that, after a change of variables, the quantum knot invariants (Jones, HOMFLY, Kauffman, etc.) can be written as power series whose coefficients are finite type (i.e., Vassiliev) invariants. But what about their categorifications?

Specifically, do the generating polynomials of dimensions of the Heegard-Floer, Khovanov/Khovanov-Rozansky, etc., homology theories admit a change of variable such that the coefficients of the resulting power series are finite type invariants?