I FIGURED THIS OUT! At least partially.
This happens on one of my clients 100% of the time when holding down a keyboard key, including backspace/delete, arrow keys, etc. This is 100% repeatable for one of my systems, though I have no idea why it's not repeatable on my second client. But at least I now have the trigger.
Can someone else who is experiencing this issue please confirm on your own system if it's the same?