From 45 years of helicopter flying, 40 of them offshore, I would say that you are stretching things to say flying to an from an island in the middle of a lake counts as offshore flying. Sure, if you are operating to a rig, semi sub or diving vessel.
Also I think you are stretching the long line bit again. I had a lot of experience of underslung load lifting but no long line experience but I knew many who were experts at long lining. I think banner towing, again is stretching a point.
This is my personal interpretation of the two but I am sure there are many out there who will be able to quote you chapter and verse on the legal or official definitions of both
John