If the only remedy is monitored end of term exams, so be it.
At some point in college when I was thinking about law school, I learned about the Socratic Method. It was weird because up to that point in college, I just pretty much flew under the radar and took exams. It was far different than high school, and I realized my high school did pretty much use the Socratic Method. It wasn't as intense as law school, but every class, maybe 4-5 people would we grilled by teachers. This was called "participation."
Shy? Anxiety? Yeah, that didn't matter. Your number would eventually be up a few times a month. You had to prepare and know the assignments, otherwise your grade would suffer and public humiliation was a real thing.
If you take away the credit given for homework, you still can give feedback, while removing any incentive to cheat.