Just stated with Tornado and loving it so far. I ran into the "task was destroyed but it's pending message" yesterday and it's causing some performance issues on our application where requests are stuck pending until timing out. I've tested your fix:
https://github.com/tornadoweb/tornado/pull/3269 and it's solved our problem. I'm wondering if there are plans to bring that commit over to the 6.3 branch, so it is included in the pip package? I'm happy to open a PR for this, but not sure how you decide what to include in each release and if this is in scope.