The following papers seem to be related to your result.
R. Fenn and V. Turaev, Weyl algebras and knots. J. Geom. Phys. 57 (2007) 1313-1324.
V. Huynh and T.T.Q. Le, On the colored Jones polynomial and the Kashaev invariant. J. Math. Sci. 146 (2007) 5490-5504.
They give an expression of the colored Jones polynomial using a determinant of a matrix involving some construction using q-Weyl algebra, and if we set q=1 we get the Alexander polynomial.
It seems to me that these results are similar. To justify the novelty of your paper, it would help to explain how its contribution improves upon these previous results.