Interesting use case, but I can’t think of a workaround solution.
If personal messages are disabled globally, then that includes personal messages in groups. I just tested it in my site, it’s a bit confusing because you still have the “Message” button available in the group page, but you will get an error when trying to send the message.
I think you will have to create a private category for the group, and then delete it once the event has finished.