Will there ever be a way to "customize" the way the pause menu looks?

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You can customise the text and colour of the in-battle pause screen only. The chequered background uses the textbox1 background colour, and the text is the normal text colour, both of which can be changed in the UI colours editor. You can change the 'PAUSED' text in the Global Text Strings editor.

Right now, it doesn't seem like there's demand for more customisability.

In the new Voxhumana version, you can change the looks of the pause menu.