Possibly add the help icon to the "beta" label, and have it as an option in the menu?

That sounds good. The link should probably be something like [[mw:Special:MyLanguage/Help:VisualEditor/User guide]] and live in a MediaWiki: interface message, so that wikis can customize it to link to a local page.

My feeling is that the link to the user guide should persist even after we're out of the beta, but we can discuss this then.

Change 71376 had a related patch set uploaded by Jforrester:
Add user guide link to beta icon drop down

https://gerrit.wikimedia.org/r/71376

Change 71376 merged by jenkins-bot:
Add user guide link to beta icon drop down

https://gerrit.wikimedia.org/r/71376

This has been done and will go out later today.