John Stevens tipped me off to using g(Math) to add handwritten responses to Google Forms. This morning John sent me a direct message on Twitter to tell me that you can now use handwriting in Google Documents through the g(Math) Add-on. John wrote out step-by-step directions with screenshots here. I made a short screencast of the process. That screencast is embedded below.
Thanks again to John Stevens for the tip. And thanks to John McGowan for developing g(Math).