Another thing you might do, especially if you're there every day or nearly every day, is fill up a hay net or two with extra flakes for overnight. That way, he'll have something to eat and stay occupied with, but won't be wasting as much or making a mess of his stall (which might help you with the other problem if he's just being messy with his eating).
My boarding setup is pretty much the same as yours. My mare was eating all her overnight hay by about 8pm every night until it was put in a hay net. Right now, she's the only one who uses a hay net, and I offered to fill it myself when I asked for her to have it, but BM said no need, the barn assistants take care of it. Which I very much appreciate! But even if your BM can't make that happen, maybe if you can fill it up whenever you're there during the day, they could hang it for you at night check?