Pics are sometimes not very clear, but while he's not thin at all in the 'before' shot, it appears he is not too obviously overweight in the after. I wouldn't think he needs to lose too much. Therefore, he's probably getting a reasonable amount of feed & calories. Now that he's in more work(I'd be careful about exercising a youngster under saddle too much, would favour other exercise & training more until the horse is matured.), you'll probably find he'll slim down & tone up a little more on that much feed anyway.
I agree, you definitely don't want to give him any more grain(I'd avoid it completely) and with no pasture, he'd likely need the vast majority of that much hay daily, if not all. 'Hay bellies' may be unaesthetic to some, but it's grain/starchy rich feeds that cause so many health problems. If you were to put his hay in small holed hay nets, you will still be able to feed him free choice, but may find that he eats less, as he can't gorge himself on it.
I'd consider just giving him the hay, including some alfalfa in the mix too, and cutting the hard feed all together, with the exception of a nutritional supplement, perhaps in the form of a pelleted 'ration balancer'.