This use of "very not appreciative" caught my eye on Sunday:
“I’m very not appreciative of the way she came in here,” Ted Shpak, the national legislative director for Rolling Thunder, told the Washington Post.
This construction is not in my own dialect; it reminds me of the recent broader uses of "so". ("I'm so not ready for this", which I had perhaps mistakenly been mentally lumping together with "That's so Dick Cheney" or "That's so 1960's".)
I'm not sure what's changing, "very" or "not" or both. I suspect that "not" may be moving into uses previously reserved for "un-".
One fully standard form is "very unappreciative", but that seems to have a different meaning, where someone is not appreciating something they should appreciate (like their mother).
Another fully standard form is "not very appreciative", but that certainly has a different meaning, just negating 'very appreciative' rather than the intended intensification of 'not appreciative'.
To get the intended meaning within my normal range of options I would have to use the wordier "I very much don't appreciate ..". So the new form (if it is indeed new) does seem to be useful.
I would guess that more people can use "so" this way than can use "very" this way. That would suggest that it's "very" that's changing rather than "not". But I'm not sure.