If the refusing is not pain related, rider related (confusing the horse) or tack related, then a lot of times it is better to ride in different environment for awhile to give the horse a mental break. So many times focusing on an issue and drilling makes things worse. It often works to go on a few trail rides and get the horse doing different things. Then when you go back into the arena the horse has learned more and understands the cues better and the issue is resolved without even working on it directly.
It concerns me that the horse dragged his feet when being led. This sounds very much like the horse has bad feet or a sore back. It is more difficult to do smaller circles and arena work for a long time for a horse when they are out of shape. The horse sounds like he is either in pain or exhausted.
Also think hard before you decide you want to use backing as a punishment. I have seen several horses now that have been taught this way and they will begin backing rapidly when they are confused. This is unsafe when you are on a trail ride or riding with others because the horse can keep backing into other horses or toward a ditch. It is very difficult to stop a horse from backing. It often works better to turn the horse and circle instead, if you want to keep their feet moving. Just don't insist on it too much or you will have a horse that spins when confused instead.