I have a paint that I train for WP. Not only does he have a naturally low headset, he also has a pretty thick-but-long neck. This causes problems when it comes to collection. :) Good for you for not wanting to just pull his head up!
Here's his 'low' head position:
And that's where he likes it. :) But in order to get him in shape for WP and Huntseat, I work him 'up' like your describing, like so:
Not our best picture, but I'm sure you get the idea. ;) His head set comes up a little higher with consistent, careful work.
The first thing you'll need to do is carry a dressage whip (unless your boy likes going forwards). Start at the trot (the walk will be the hardest), and push him into a really nice purposeful trot. Not something that /rushes/, think of big, long, powerful steps. Do NOT lean forward. The moment you do, your horse is going to go, 'why bring my head and chest up if she just leans on it??' Usually, when you push your horse forward, his head will come up.
...And, it might only stay there for a few strides, because he thinks to himself, 'this is a lot harder then what we used to do!' Not only does he have to learn to push off his hind end, but he has to OVERCOME his conformation and pick up that head and neck. When the head comes down, use your legs first to encourage him and the dressage whip ONLY if you have to to get him to bring his head up. Only work on this a few minutes a day, and only when he's fresh (asking him to do it after he's tired is mean and you won't get what you want!). Stay at the trot and canter in the beginning.
DON'T fuss with his head in the beginning, just make sure he isn't sticking his nose out and hollowing his back by trying to encourage the looong movement, and the long neck forward. Squeeze one rein GENTLY if he locks his jaw up and release when he drops his nose somewhere around vertical. Really don't pay attention to his head for the first couple of weeks though!
As he starts learning his 'new' job, you won't have to encourage him so much. It is hard for them when they start out, but it is possible to get them to carry their head higher with correct work. This is, of course, the simplified version, so if you try it and run into snags, let me know and I'll explain anything further!