You are straightening your arm too soon. You need to drive your elbow forward towards the target as long as you can and let your arm extend (open) on its own. This will typically be when the disc is somewhere around your left pec. You extend your arm way back at your right shoulder, and you then have to swing it around in a wide arc and try and release the disc at the perfect moment of that arc.
Watch Paul's elbow in this video. See how it drives forward toward the target, and how it makes his arm bend in and the disc move in a straight line until it can't go any farther forward (at his right pec)? At that point his arm extends (swings open) and you can see the crazy acceleration as it opens back up on its own. His shoulders open up to counteract the arm opening and the disc therefore stays on a straight line.
Best thing to do is to go out and just drive your elbow at the target...literally use your elbow to aim. Don't think about the disc at all, other than to hold onto it with a firm grasp with a stiff wrist. Just get that elbow driving on a line towards the target. See what happens. Your arm should open on its own at the right time and the throw should be online. If it's not online, get in front of a mirror (without at disc) and check your body positioning and your elbow to make sure that what you "think" you're doing is what you're actually doing.
If you're successful, you can start working on ways to strengthen that elbow extension and incorporate the hammer drills to strengthen the wrist extension as well. The hammer drill is excellent but I don't think it will help much if you don't get some bend in your arm.