I would like to realize a symbol that looks similar to a `\Pi`, but with its two legs crossed, like in an `\mathrm{X}`. In other words, I want the bar in `\overline{\mathrm{X}}` to be moved down just a little bit, placing it on top of the `\mathrm{X}`. Here is what I achieved so far, using code from [Moving the bar on hbar](https://tex.stackexchange.com/questions/30291/moving-the-bar-on-hbar):

```
\documentclass{article}
\usepackage{mathtools}
\usepackage{xparse}
\makeatletter
\newcommand{\raisemath}[1]{\mathpalette{\raisem@th{#1}}}
\newcommand{\raisem@th}[3]{\raisebox{#1}{$#2#3$}}
\makeatother
\NewDocumentCommand{\crossedPi}{}{
  \ensuremath{\mathrlap{\raisemath{-1.6pt}{ 
    \overline{\phantom{\mathrm{X}}}}}\mathrm{X}}}
\begin{document}
  $\Pi \crossedPi$ \\
  $\mathrm{Set}_{\Pi} \mathrm{Set}_{\crossedPi}$
\end{document}

```

[![enter image description here](https://i.stack.imgur.com/HBdyc.png)](https://i.stack.imgur.com/HBdyc.png)

The `\crossedPi` symbol in normal position looks just as I want it to look, but when the symbol is used in index position, as in `\mathrm{Set}_{\crossedPi}`, the bar gets out of place.

What would be the perfect professional way to realize this symbol in a robust way, so that nothing gets out of place when used in index position?