What you should do, is sit down, and bring your leg up to 90 degrees on the matt and then slide his knee off you. Thats the best technique of escapeing the half gaurd
The way this works: you're in deep half, he leans forward, and you come out the back. The standard back take is to use a hook to try and lever his leg, preventing him from turning into you, and take the back from there. The problem is that it's very hard to prevent that turn. Instead, keep your front leg locked around his and don't try to go directly to his back. Reach over his hip, and lock your hands around his opposite leg. Now, roll over your shoulder that is closest to him to get to a banana split type position. From there you can spin him into full back control. Ryan Hall doesn't specifically show this on his DVDs, but the rolling back to is shown on his Back Attacks DVD, and the position is pretty easy to get to from deep half. He actually does it in the well known 'path to the back' clip from his match with Hermes Franca. I'd study that vid a lot and try it a few times. This is the only way I can consistently take the back from deep half.
I actually like deep half a lot. If I see an opening I go right for it and attack with a sweep.
If you're allowed, the "dog-bar" is a really easy knee bar to hit from DHG, and few people see it coming.
No idea what it's really called. I've heard it called it a "reverse knee-bar", "dogbar", plain ol' knee bar, and "that knee bar from half guard".
I've looked on line and dog-bar is the only name I can find.