Viable alternatives to Forms for classroom quizzes?

The lack of any ability for a student to log out of Forms after completing a form makes it a complete non-starter in a school environment with shared devices.

What are some alternatives that might work?  I'm just looking for a simple multiple-choice quiz web form that self-grades at the end.  Ideally something we can integrate with Sharepoint or some other product within Office 365 where there is support for logout.  Prefer something ad-free or that can be self-hosted.