I have to keep mine on a track system, it basically limits his grazing but encourages continuous movement. I used to have to lunge 2-3 times a week but I don't have to worry at all when he is on track. Its fiddly and time consuming to set up and most livery yards probably wouldn't want to...
Ditto what others have said about worming and sufficient nutrients in diet.
But trying him on a track system would also be worth looking into, will improve his overall fitness without actually exercising him but will also limit his grass intake.
I didn't box rest at all, sectioned off a small bit of field at first but she just seemed to get worse, the pain was enough to limit just how much she moved about so I gave her the choice, I had the support of an amazing trimmer who came weekly to check the changes in her feet. She had AdLib hay...
I'd second looking at setting up a track system/paddock paradise in the paddocks. Definitely works a treat limiting grazing but encouraging movement, get it started now and get her out on it asap. The movement will encourage the blood to keep pumping which is essential for recovery, the longer...
If I were you I would contact a DAEP barefoot trimmer. Its hard to tell from the photos but it looks like the whole balance is out, heels have come forward and look long, which will mean extra loading down the back of the limbs. The toes are far too short, and the side walls at risk of splaying...