I have been patiently waiting for this. Google Forms has added a new feature that allows you to collect documents! See this help site to learn more: https://sites.google.com/site/scriptsexamples/home/announcements/google-forms-file-upload-feature
Caveat for BV users. You can’t share this with your students since they are in a different domain. Staff can share with staff. Here is an image that may help you understand the issue.
If you are unfamiliar with Google Forms, see this video! It upgraded in 2015. This video helps you with these changes as well.