General expression for non-unity gain feedback system's steady state error with disturbance
Starting from the system equations (upper caps for transfer functions, lower caps for signals):

$$
\begin{cases}
e = r - Hc\\
c = G_2(d+G_1e)
\end{cases}
$$
$$
e = r-HG_2d-HG_1G_2e
$$
$$
e = \frac{r-HG_2d}{1+HG_1G_2}
$$
$$
e = r\left(\frac{1}{1+G_1G_2H}\right)-d\left(\frac{G_2H}{1+G_1G_2H}\right)
$$

In comparison, your method is too convoluted, but I followed the development and believe the issue lies in the very beginning, moving \$d\$ to the left of \$G_1\$. This ends up changing the error signal to $$e = r+\frac{1}{G_1}d-Hc$$, which is incorrect.