Yes I was going to suggest that the token root plugin would solve this - but it appears Sam has already tried it. I know build root token plugin has worked for other identity providers.
Based on: https://issues.jenkins-ci.org/browse/JENKINS-25791 - it looks like it is not related to PR#37 - but do you want to try an older version to check? It can't hurt. Maybe some special case code is needed for this.
I don't think people come across this a lot as they tend to either a) use a github oauth token to interact with jenkins or b) use github to trigger builds directly.
If we can confirm it isn't a recent breakage perhaps should close this as a dupe of #25791 and move discussion over to there?
What token are you using? A Jenkins generated token or a GitHub personal access token?
ViewedStatus option only takes effect if you have the Embeddable Build Status Plugin installed. It has nothing to do with triggering builds.