To close the loop here, I got the following response from Jack/Allen & Heath support via a support ticket. In case anyone else faces a similar issue, here’s how to permanently delete the logs from the mixrack:
If you navigate to the history tab, and click the ‘Setup’ button to the left of the screen, you should see an overlay on the history log in blue that says “Event Logs”
Clicking this will show a menu in which you’re able to enable “Show all Event Logs”
The button that previous said “Clear Logs” will now read “Delete Logs” and you will be able to permanently delete the log history.