Looking at the blowup, it looks pretty simple. Still remove the cable from the holder where it attaches to the carb and work it by hand. Then you can isolate the problem either at the trigger or at the carb.
I'm probably not communicating my problem properly. Take a close look at the second image I posted above. With the trigger partly depressed and NO SCREW in the screw hole in question, the end of the trigger can be seen in the center of that empty screw hole. If the screw were in it, the trigger would stop there. At that point the throttle cable would have barely moved from the idle position.
If you are installing the screw with the trigger in this position, that's incorrect. The upper portion of the trigger will hit the screw before the engine even leaves idle. The upper portion of the trigger should be on the other side of the screw.
The throttle trigger should be right up against the handle at full throttle (my 1st pic.) When released, it comes down until it hits the screw, by which point the engine should be at idle. The screw is what keeps it from coming down too far (2nd pic.) If the screw is overtightened, the trigger won't be able to return far enough and your engine will not slower than 1/3 throttle.
Now things are starting to make sense. There is some resistance when releasing the trigger so I just ordered a new cable. I think it got pinched where the shaft meets the engine.
Thanks so much for all the help. Very much appreciated.
Just to close the loop, my handle and throttle cable arrived and have been installed. The edger now works great.
Thanks again everyone for your help. Very much appreciated.