No to the molasses. Stay away from sugars all the way around. He's not "getting bored" of the hay, he just doesn't want anymore at that particular time. Horses don't get bored of eating. That's what they do, all day long if they can.
Minerals -- I wouldn't change that either just yet. Eliminate the sweet feed and give him hay in front of his face ALL THE TIME. If the hay is gone, he needs more. If the other horse shouldn't have access, then you need to separate them. Might not be easy, but forage is the number one way to help your underweight horse.
That said, you could consider that he might have other issues as well, so by simplifying his diet you may find other answers. I personally would give him all the hay he wants, and more. Beet pulp twice a day, maybe some rice bran in there too. Minerals and water he has, so that's good. 24/7 pasture is also good.
As mentioned before, being a TB is not a reason, it's an excuse. Being an individual with individual needs is a reason and you have to deal with that.