TikZ-Cd – Drawing a Bent Arrow Under a Node

tikz-cd

Here is my problem.

Problem

I am trying to get a bent arrow "go" under the CxExF node by breaking the long arrow into two parts. However, I would like the two parts to follow the same "path" as the long arrow. This means that I would need to move/shift the entry (and exit) point of the two parts so that it looks as the broken arrow is really passing under the node. To give a sense of what I mean, I include below what would be desirable, (generated using an image editor). Any suggestion? Any better way?

Desired solution

Below the code generating the issue.

\documentclass{article}
\usepackage{tikz-cd}
\begin{document}
\[
\begin{tikzcd}
        X \ar[r] & A &\\
        & C\times D\times F  &\\ 
        &   &\\
        &   &\\
        &   &\\
        &   & B \ar[luuuuu, bend left, in=190, out=10]
\end{tikzcd}
\]  

\[
\begin{tikzcd}
    X \ar[r] & A &\\
    & C\times D\times F \ar[u, bend left, in=240, out=0] &\\ 
    &   &\\
    &   &\\
    &   &\\
    &   & B \ar[-,luuuu, bend left, in=190, out=10]
\end{tikzcd}
\]  
\end{document}