stix package in nomath mode

Question

I have a big physics book typed in latex with standard fonts, including many math font packages (bm, double strike, ams, etc.). The manuscript has been checked carefully by several readers.

The editor says that they wish to switch to the STIX fonts. I checked that this introduces many problems in the formulas; for instance, the simplewick package does not work well anymore (I can give more details on these problems if anyone is interested).

I thought that the solution was simple: use STIX in the nomath mode, so that only the fonts of the text should be changed:

\usepackage[nomath]{stix}

I was naively expecting that my formulas would be treated exactly as before using STIX. In fact, this improves the situation a lot, but some serious problems remain. For instance the commands \gtrsim and \leqslant seem to be no longer recognized.

Am I doing some trivial mistake? Many thanks in advance for any advice.

Franck

Here is an example:

\documentclass[a4paper,twoside,10pt]{book}
\usepackage[nomath]{stix}
\usepackage{amssymb}
\usepackage[fleqn]{amsmath}

\begin{document}
Some text to see the fonts
$ a \gtrsim b $
$A \leqslant B $
\begin{equation}
\lvert(\psi_{1},\psi_{2})\rvert
\leqslant
\sqrt{(\psi_{1},\psi_{1})}\;\sqrt{(\psi_{2},\psi_{2})}
\end{equation}

\end{document} 

---

@JoKalliauer Thanks Jo for your kind interest! I was handling two volumes of a quantum mechanics book, about 1500 pages, which have been typed in latex with standard fonts. Using stix fonts is easy, and creates no problem in the text. On the other hand, it does introduce problems in some equations: because the size of the fonts has changed, some alignments are destroyed and the equations become harder to read (Wick contractions actulally become impossible to understand). I thought that the solution was to keep the stix fonts for the text only, and use the [nomath] command. Alas, this does not work: the equations are still modified with this command, for some mysterious reason.The final result is that I told the publisher that it was not possible to use the stix fonts, and they agreed - there was no other solution anyway, except retyping too many pages. Still, this seems to mean that there is something wrong with the [nomath] command.

Thanks again! Franck