Problem with "not" in full text search
I'm not super familiar with full text searches but I think this StackOverflow answer gives us the answer which is also supported by this StackOverflow answer.  The solution was to create a computed column containing what is essentially a concatenation of all the columns you want to apply your search terms to and do your full text search on that column.

Alternatively you can use the AND, OR, NOT logic in separate expressions like the OP in the StackOverflow answer I linked to.

That being said someone here might have a better solution.