Calling all tweakers...help!!

Like so many on this board I’ve become a tweaker, and gotten fairly good at it, I think. I usually apply the guitar pick tweak (amongst others), but I use a piece from a drink bottle. I’m sure you all have noticed that the “guitar pick” tweak tends to flatten the whistle from 10 to 25 cents from the intended key. No problem…my usual cure is to cut a pice off the barrel at the fipple end. But I just tweaked a non-tunable Kerry “Songbird” aluminum alloy whistle. Ooops, no cutting pieces off here. I’m fairly certain there is no cure, but it’s worth asking. Any answers? And I’m not adverse to radical surgery in this case, because I had basically given up on this whistle until the tweak solved the problems.

Why didn’t, or don’t, yous send it back to the maker ?

Two reasons:
A: last time I did that, the one that came back was worse than the first. (Different maker, less expensive whistle)
B: I am convinced that the Songbird’s performance is normal for this brand.

HOWEVER, your idea is not a bad one. I’ll think about it. Thanks for the good thought.