Don't think of it as throwing the disc, think of it as your throwing your elbow forward, after which the arm will whip around like a trebuchet, which will fling the disc forward.
To do that, you need to think of the reachback in terms of the elbow, not of the disc. So you reachback your elbow such that it has a long way to travel before your disc reaches the right pec. This will necessitate turning your shoulders back farther than you have so far.
So from the back of your reachback, until the disc is infront of your right pec, your wrist/forearm/disc are just kind of along for the ride. There's a small amount of effort to keep the disc level, and close to your body, but otherwise it's all elbow forward.
From here, your shoulders should be pointing mostly in the direction of your throw, the disc should be at your right pec, and your right hand should be on the outside edge of the disc.
You unwind from that position. I found that it was much easier to hit that position going very slow, and then once I had the basic idea down, throw slow approach shots, just focusing on getting your body into the right positions. And as you start putting some muscle memory into it, you can speed it up a bit at a time.
Your release should be pretty far out infront of your body. It's pretty easy to go through all that, and not get your arm out infront, if you don't think consciously about extending your arm forward. You don't lock your elbow, but you do pretty much want your arm extended out towards the target.
