I did some poking around in the SVG file generated by Affinity Designer's export function. I found that the output SVG "width" and "height" attributes were set to "100%". Looking at the SVG that is output by Inkscape, these are set to absolute dimensions. As an experiment, I tried editing the SVG file from Affinity Designer, and changing the height and width to
<svg width="8.5in" height="11.0in">,
and, Voila! My file imported into Carbide Create 3D, scaled correctly! Note that I had set my Affinity Designer canvas to 8.5x11 in, so this matched the size of the canvas.
I should probably try a few more files just to be sure this works the way I think it does, but it looks like this may be the answer.
Edit: Yup, that seems to do the trick!