I've been experimenting with putting my right (bottom) hand pinkie finger on the bottom of the whistle, below the bottom hole. My teacher had recommended that I do this ages ago, but it never felt natural, and putting my third finger down on the bottom hole when I play a C♯ (or sometimes B, etc.) always seemed to work well enough.
Until The Atholl Highlanders. Playing A-c♯-e repeatedly is just a lot easier when I don't have to have my bottom-hand third finger moving. And similarly for some other parts of that tune.
Update: I received a suggestion in private email to try a different technique with The Atholl Highlanders, which helps even more. But I still find the pinkie helpful in this and other tunes.
It still doesn't feel quite natural, but it's a lot easier to play some phrases, and I think I can keep the whistle steadier this way.
This is (temporarily, I hope) somewhat confusing at the moment. I'm having to relearn certain passages to make optimial use of the new grip and I'm tending to grab too hard with my right (bottom) thumb and pinkie right now. But when I do it right I'm finding that some passages just come out a lot cleaner, like the second to last measure of both parts of Harvest Home.