Reusing decorated path

Question

I am currently trying to create a freehand style as seen in technical drawings:

(see the thin line to the right of the shaded part)

This is what I have so far:

\documentclass{article}
% https://tex.stackexchange.com/questions/586063/reusing-decorated-path
\usepackage{tikz}
\usetikzlibrary{decorations, decorations.pathmorphing}
\tikzstyle{freehand}=[decoration = {random steps, amplitude = 10}]
\begin{document}
\begin{tikzpicture}
    \draw[thick] (0, 0) rectangle (6, 3);
    \draw[thin, freehand, decorate] (3, 0) -- (3, 3);
    \fill[red, opacity = .5] (0, 0) -- (3, 0) decorate [freehand] { -- (3, 3)} -- (0, 3);
\end{tikzpicture}
\end{document}

This somewhat does what I want:

However, the line and the background don't match.

I think I can fix this through either

1. setting a random seed to the same value for both parts
2. use filldraw from the beginning
3. name the random path & reuse it for the fill command

I couldn't find any way to do 1.

2 I don't like because there could be situations where I want to fill both sides of the lines.

So my question is, how do I save a morphed path to reuse it later?

Thanks in advance.