While further developing my printed-circuit-board method, I inadvertently figured out how to do filled shapes with the pen using the free version of "Eagle" PCB design software.
1) You'll need to have Eagle (free version is fine), Inkscape, and Make-the-Cut all installed and available. I use Gimp for editing and converting file formats.
2) Open the desired image in Gimp (or other image editor) and save it out as a BMP format image, with as few colors as possible. A 1-bit monochrome with no dithering is best, like line art. (you set this via Image->Mode->Indexed... in Gimp)
3) Start up Eagle, and do a New->Board.
4) Do File->Run, and run the script "import-bmp.ulp". This will be located in the ulp subfolder of your Eagle installation directory. It will prompt you to browse to your BMP file and open it. Keep your bitmap size modest, 300 DPI or less, more just slows everything down. If you have a black-on-white drawing, select White only and click OK. Click the DPI radio button under Format, and set your DPI value; it will set the Scale factor for you automatically. Click OK.
5. It will think and popup window saying "Accept Script?", click "Run script".
6. Your bitmap should now appear in blue in the Eagle Board window. Save your project, then Run File->CAM Processor.
7. Select Output Device HPGL. Deselect all layers except #200 "200bmp". You'll have to scroll down to find it. Click "File" and browse to your desired output file location and name. Be sure to give the file a ".plt" extension which indicates the HPGL file type. Set the Pen Diameter to the actual width of the line your pen produces. 1 mil = 1/1000 inch. A ballpoint pen tip ranges from about 20-50 mils. Click "Process Job". This will render your .plt file.
8. Start up Inkscape, do File->Import... and import your .plt file. This can take a little time. If the application freezes, give it some time.
9. Eventually, your image will appear in Inkscape, already selected. Click "Edit->Copy".
10. Switch to Make-the-Cut, now do "Paste-in-Place". Voila!
Note, depending on how large the filled areas are, and the diameter of the pen, it might take quite a while to calculate when you click the "Cut Project With..." button. (the example image has 65000 points). Fortunately, since the fills are done using mostly horizontal and vertical lines, the machine can run pretty fast.
Here are another couple screenshots to show the pattern closeup. If you wanted a grid you would tell Eagle that the pen is wider than actual.
This method should work really well with engraving tips..
MTC reported this image was about 11000 cutting points which really seems pretty modest to me. I haven't tried actually printing one this big yet. If you (in MTC), right click on the imported image, and do Shape Magic->Advanced->View Path Detail... and scroll down through the path segments with the cursor key, you'll see the path taken is pretty sensible and doesn't waste a lot of time scrolling wildly all over the place.