After some searching around, I learned that I need to get the MPEG-DASH functionality turned on. This can be found in the Youtube plugin settings, but it is grayed out by default. After some more wild flailing about, I finally got it working, something like this.
- The "kodi-inputstream-adaptive" package needs to be installed from the Raspbian repos. It doesn't get pulled in as a dep of Kodi.
- The inputstream plugin now needs to be enabled. Start Kodi and go to the settings menu. Select Add-ons, My add-ons, and VideoPlayer InputStream. Here you will find the InputStream Adaptive plugin. Click on it, and select "Enable".
- You should now be able to go back to Youtube and enable MPEG-DASH. I also installed the Inputstream Helper plugin from that menu, but I'm not sure what effect it has.