In fact, you would be far better off 'playing' with your outside rein, though I don't necessarily advocate either. If you want a nice "headset" you should allow the horse to find it himself. When we train all of our greenies, we basically give them their head until they build their balance, and then touch both sides of their mouth to coax the head to a more accepted place. Obviously, the greenies can't hold the roundness, but this creates a situation where, rather than putting their head to a place they think it should go, they put it where it is comfortable.
I try to advert the use of the word of headset, simply because when people around here hear that, they immediately move to draw reins and tie downs. So that may just be me.
Despite the word used, try to dismiss the notion of keeping the head down, but rather working from back to front, and pushing the horse into the bridle while bringing the power from the hind end. The horses that are round this way are the very most correct and will move up the levels much easier.