Why not run a trellis on top of the fence and use vines to cover it . Then you would still have space for maybe aa small patio for the BBQ and a couple of chairs or a small outdoor kitchen type layout. Check what vines are evergreen in your area ,the bonus is they will also cut down on road noise .

If cars are flying over the fence, you have to call authorities.

Since your pictures only show ground, not what would be screened or the space available above ground, it's not possible to say what kind of tree might work. Show the overall space and the offending object(s) to be screened.

Too bad the neighbor's row of Thuja does not come all the way along his side of the fence. The trellis idea is a good way to get instant relief. Without having a lot of space be eaten up by a hedge - after waiting years for it to size up.