fill in svg or stl design
If you don't mind adding another tool to your toolbox, you can use a plug-in for Inkscape called Inkscape OpenSCAD DXF Export that will convert your SVG drawing to appropriate code to import to OpenSCAD. Even if you aren't keen on learning OpenSCAD, once you have the code, press F5 for a preview, F6 for a rendering and then export the STL file.

The link on Thingiverse gives instructions how to add the plug-in (extension) to Inkscape, which is relatively simple. I've been using the extension for applicable projects with great success. Expect minor complications for closed paths within other paths, however. You may have to create separate STL files for those paths and use Boolean subtraction to remove the "holes" as needed.



The extension is slightly counter-intuitive. Be sure to manually add the .scad extension to the file as it does not perform that task automatically.

UPDATE: I have discovered that the above link is not the one I've been using. I'm leaving it in place as it may be useful to others to have the ability to create .DXF files from Inkscape. The correct one is called Inkscape to OpenSCAD converter v6 and works as described above.

As always, read and follow all label instructions. Do not operate heavy machinery after using this product.