Jumping in late here, but
that your lousy neighbor is moving.
Now, if you have something really nice planted along the offending foot of property between their fence and your line by the time the new owners move in, unless the new neighbor is as nuts as the old one, I am sure they'll be too busy with their new house to worry at all about what is planted against that fence. In fact, I'd be more than thankful that you were taking care of that space.
You can work away at putting in your raised beds in your own time. Maybe the new neighbor would be amenable to the idea of just moving the fence to the property line? The posts are probably cemented in, but that's a lot less hassle than putting in a whole new fence!
