Can you make an example that shows it not working properly? I know it's not perfect and needs some tweaking, but I think it's at least adequate. If you move an object and there's no obstacles involved at all, even with pathfinding on the movement should just ignore the grid and move directly to the target.
The best thing to make movements more efficient is to increase rotation speed like you said, and reduce the 'Blocked speed', which is the speed it reduces to if it finds itself pointing in the wrong direction or unable to reach the target.