We have a Welsh C pony who has always boxed walked (in the same direction as well) - we've tried various things to stop it (stable lick, nut ball etc) but nothing has ever cured him of it (he's 16 now so I don't think he's going to change!) It's only worse in the winter when he's on part livery - in the summer he mostly lives out, so it's not an issue.
living out is the best plan for horses that box walk, we have a mare in the riding school who kicks so cant be tied with other horses, we can only stable her for the 10mins before a ride leaves then she needs turned out again!
she gets really stressed and goes round and round then starts charging at the door so its alot safer for her to be outside 24/7.
I look after one mare who actually canters around her box! Not all night thankfully, but her box is a state every day. Luckily, she lives out most of the year
I'd be surprised if you manage to cure a confirmed box walker.
My youngster used to box walk, she lives out 24/7 in the summer and in at night in winter. I bought her a stable mirror and box walking disapeared over night!
The mare I've had on box rest for four months now used to box walk badly all day but not much at night. As she had to be kept still we put a stall guard up and rings and cross tied her in front of the doorway. We hung haynets on each side and frequently offered her water. After a week we didn't tie her and she had pretty much stopped doing it. She never used to stand still except to weave but now only walks when there is extreme provocation - like mealtimes. The weaving is greatly improved as well!
I have to say she was also ACP'd.
It is interesting though because I thought that it was a stress habit and couldn't be unlearned and that she'd express her stress in some other way. She doesn't seem to.