So I figured out how to do this with Inkscape, it's just a bit wonky:
1. Make your shape as a simple path
2. Set the size of the shape to be between 0 and 1 (width and height) in some base unit
3. Set up the document so that the scale is 1 of whatever your base unit is.
4. Save an optimized SVG (not always necessary) to get a maximally simplified path (with no transforms or whatever).
5. Open with a text editor and copy the path into your `<clipPath>` SVG.

If that doesn't work as expected, you may have to copy the path and paste it into a new document after it's been scaled and moved.

If that's still not working, you can copy-paste the path into this tool and play with the scaling: https://yqnn.github.io/svg-path-editor/