Conjectured enumeration formula for 20-vertex configurations and Aztec-triangle domino tilings

For each $n\geq 1$, let $Z^{20V}_n$ denote the total number of 20-vertex configurations with DWBC3 boundary conditions on the quadrangle ${\mathcal Q}_n$, and let $Z^{DT}_n$ denote the total number of $2\times 1$ domino tilings of the Aztec triangle ${\mathcal T}_n$. Enumeration conjecture. The two numbers coincide and are given by

$$Z^{20V}_n=Z^{DT}_n=2^{n(n-1)/2}\prod_{i=0}^{n-1}\frac{(4i+2)!}{(n+2i+1)!}.$$

The formula is presented as conjectural in the concluding discussion and is supported there by numerical data; the supplied paper proves the corresponding identity for the cases $k=1,2,3$, but does not establish this exact product formula in general.