How do I remove a font's math metadata?

You can always use the NewComputerModern font as an ordinary font, by selecting it as the current font in the Home pane. You are not obliged to use it only as a Math font.

You may set another font as the default Math font in the Conversions dialog.

As you say that Word insists on using this font whatever your setting, you may need to edit the OTF file.

I tried, for example, with the file NewCMMath-Regular.otf, to edit it using the free online editor at Glyphr Studio and gotten this interesting page:

This might be a way to create a new font that is not mathematical. I haven't tried to go all the way through to see how it works, but using the above options and saving the new font was already pretty slow.