Font Size appears to be awry.

I work in the sign industry and some of the stuff I create gets sent to routing tables (in the form of G-Code). By the time the graphics get to that stage the fonts are no longer "live" but just raw vector outlines. I typically set the size of my lettering in inches and using the cap letter height for the size reference. Units based in Points and invisible Em squares are fine for grid-based layouts on printed paper. It doesn't work so well in sign design. The cap letter height, baseline and distance down to the next cap letter height line is easier to define since those boundaries are physically visible to fabricators.

If you size letters using the cap height options and are able to use inches as the unit of measure the letters should end up in your cutting software without any scaling issues.

Dave,

As I (mis)understand it, how about your using one of the following ways depending on version and/or preferred way of doing things?

1) Draw a nostroke/nofill bounding rectangle, see here,

https://helpx.adobe.com/illustrator/using/snap-to-glyph.html

look for"/Glyph Bounds): Snaps to top, bottom, left, and right bounds of glyph."

then scale proportionately as desired by inserting desired H value in the Transform panel with Ctrl/Cmd+Enter (live Type);

2) Tick Use Preview Bounds in the preferences, then Effect>Path>Outline Object, then  scale proportionately as desired by inserting desired H value in the Transform panel with Ctrl/Cmd+Enter (live Type);

3) Type>Create Outlines, then  scale proportionately as desired by inserting desired H value in the Transform panel with Ctrl/Cmd+Enter (outlined Type).

Do you have documentation for the NC machine? What does it tell you about scaling? Or about interpretation of the files you feed it?

And check this article for font height reference:

https://helpx.adobe.com/illustrator/using/align-text.html#font-height-reference

You can set the units you want in illustrator, and even if the units is in points you can type "4" " if you want 4 inches. What can be confusing about type is how type is measured... but even here Illustrator has now the options to set the type from Cap height or X-height.
I think this video will be of help to show how https://youtu.be/M6ThX-aN9R4 (at 1:50 shows flyout menu, but look at the whole video to better understand why)

Did you check in Preferences > General > Display Print Size at 100% Zoom?

I perhaps should have mentioned that I'm determining the final vharacter height by printing the "4" to my laser printer, with no scaling, and it certainly mirros what I see on the design screen ....